Articles containing proofs | Theorems in propositional logic | Classical logic

Law of excluded middle

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 true. It is one of the so-called three laws of thought, along with the law of noncontradiction, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law (or principle) of the excluded third, in Latin principium tertii exclusi. Another Latin designation for this law is tertium non datur: "no third [possibility] is given". It is a tautology. The principle should not be confused with the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the future to show that the law of excluded middle may apply when the principle of bivalence fails. (Wikipedia).

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Set theory | Truth value | Dialetheism | Negation | Constructive set theory | Negation as failure | Theorem | Logic programming | Exclusive or | Hans Reichenbach | Tautology (logic) | Arend Heyting | Completeness (logic) | Logical consequence | Square root of 2 | Gottfried Wilhelm Leibniz | David Hilbert | Curry's paradox | L. E. J. Brouwer | Autoepistemic logic | Logical disjunction | Karnaugh map | David Hume | Zermelo–Fraenkel set theory | Law of thought | List of logic symbols | De Morgan's laws | Proposition | Finite-valued logic | Modus ponens | Constructivism (philosophy of mathematics) | Cyclic negation | Leopold Kronecker | Jean van Heijenoort | Hermann Weyl | Arthur Prior | Mathematical logic | Principia Mathematica | Irrational number | Intuitionistic logic | Problem of future contingents | Rule of inference | Law of noncontradiction | Bertrand Russell | Russell's paradox | Alfred North Whitehead | Intuitionism