Law of the Excluded Middle { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies, and introductions to philosophers, and explanations on a number of topics. Accredited homeschooling online at Northgate Academy and Philosophy online tutoring.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WTI offers immigration law course online - fully accredited. ACE credits online at EES.

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Law of the Excluded Middle

The law of the excluded middle is a law in most logical systems which states that for any proposition, either that proposition or its negation must be true.

The law of the excluded middle may be formally expressed as:

P ∨ ¬P

This is not the same as the law of noncontradiction, which states that a proposition and its negation cannot both be true. The law of the excluded middle and the law of noncontradiction may be formally represented as:

(P ∨ ¬P) ∧ ¬(P & ¬P)

Alternatively, in systems which use a symbol for an exclusive disjunction (⊕ or XOR), the laws may together be formulated as:

P ⊕ ¬P

The non-classical logic system of fuzzy logic rejects the law of the excluded middle.