Definition of Excluded middle. Meaning of Excluded middle. Synonyms of Excluded middle

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Definition of Excluded middle

Excluded middle
Exclude Ex*clude", v. t. [imp. & p. p. Excluded; p. pr. & vb. n. Excluding.] [L. excludere, exclusum; ex out + claudere to shut. See Close.] 1. To shut out; to hinder from entrance or admission; to debar from participation or enjoyment; to deprive of; to except; -- the opposite to admit; as, to exclude a crowd from a room or house; to exclude the light; to exclude one nation from the ports of another; to exclude a taxpayer from the privilege of voting. And none but such, from mercy I exclude. --Milton. 2. To thrust out or eject; to expel; as, to exclude young animals from the womb or from eggs. Excluded middle. (logic) The name given to the third of the ``three logical axioms,' so-called, namely, to that one which is expressed by the formula: ``Everything is either A or Not-A.' no third state or condition being involved or allowed. See Principle of contradiction, under Contradiction.

Meaning of Excluded middle from wikipedia

- In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is...
- the case of contradictories. Contradictories follow the law of the excluded middle but contraries do not. For example, the sentence "the exact number...
- to the use of the law of excluded middle over infinite sets. Hilbert responded: "Taking the Principle of the Excluded Middle from the mathematician.....
- of excluded middle is not taken as axiom), it is consistent to adopt non-classical axioms that contradict consequences of the law of excluded middle. Uncountable...
- semantics may or may not possess. It is not the same as the law of excluded middle, however, and a semantics may satisfy that law without being bivalent...
- derive it from the Law of the excluded middle, as follows. We ****ume ¬¬P and s**** to prove P. By the law of excluded middle P either holds or it does not:...
- the law of contradiction (or non-contradiction; NC), and the law of excluded middle (EM). Sometimes, these three expressions are taken as propositions...
- tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case"...
- still used principium tertii exclusi (the "law of excluded middle"). The principle of the excluded middle does lead to some strange situations. For instance...
- three fundamental laws of logic: the law of contradiction, the law of excluded middle, and the principle of identity. Counterfactual thinking involves mental...