The law of excluded middle (LEM) is one of three fundamental laws of thought discovered by Aristotle. It can be expressed informally as follows: for a statement to be meaningful it must be either true or false, or be composed of parts that are either true or false. Formally, this is written (P ∨ ¬P). The law is disputed in the context of many-valued logics, where rejection of LEM is thought to be a concession necessary for their realisation. I argue that many-valued logics need not (and must not) violate the law of excluded middle, and that the relevant concession involves an incorrect interpretation of the law.
The Law of Excluded Middle
The Law of Excluded Middle
The Law of Excluded Middle
The law of excluded middle (LEM) is one of three fundamental laws of thought discovered by Aristotle. It can be expressed informally as follows: for a statement to be meaningful it must be either true or false, or be composed of parts that are either true or false. Formally, this is written (P ∨ ¬P). The law is disputed in the context of many-valued logics, where rejection of LEM is thought to be a concession necessary for their realisation. I argue that many-valued logics need not (and must not) violate the law of excluded middle, and that the relevant concession involves an incorrect interpretation of the law.