For the Fargo episode, see The Law of Non-Contradiction.
This article uses forms of logical notation. For a concise description of the symbols used in this notation, see List of logic symbols.
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally, this is expressed as the 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", holds.
One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law is employed in a reductio ad absurdum proof.
To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'".
It is one of the so called three laws of thought, along with its complement, the law of excluded middle, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provide inference rules, such as modus ponens or De Morgan's laws.
The law of non-contradiction and the law of excluded middle create a dichotomy in "logical space", wherein the two parts are "mutually exclusive" and "jointly exhaustive". The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle is an expression of its jointly exhaustive aspect.
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who lived in the 6th century BCE, the implicit formulation of the lawofnoncontradiction, “‘See how upright, honest and sincere Citta, the householder...
of noncontradiction, and the lawof excluded middle. However, few systems of logic are built on just these laws. The earliest recorded use of the law appears...
mutually contradictory assertions, Q and ¬Q, and appealing to the lawofnoncontradiction. Since assuming P to be false leads to a contradiction, it is concluded...
early formulation of the lawof trichotomy Dichotomy LawofnoncontradictionLawof excluded middle Three-way comparison Trichotomy Law at MathWorld Jerrold...
Illustrating a general tendency in applied logic, Aristotle's lawofnoncontradiction states that "It is impossible that the same thing can at the same...
direct violation of Aristotle's lawofnoncontradiction. In philosophy, trivialism is considered by some to be the complete opposite of skepticism. Paraconsistent...
properties: Lawof excluded middle and double negation elimination Lawofnoncontradiction, and the principle of explosion Monotonicity of entailment and...
Lawofnoncontradiction cf. John Duns Scotus, 1265–1965 p. 250-262 Ordinatio I, d. 3: On The Knowability of God Williams, T. (2005). The doctrine of univocity...
being contrary to the LawofNoncontradiction; while the proposition one is equal to one is regarded as simply true, by the Lawof Identity. However, some...
fact that thing is an objective fact. The fallacy rests on the lawofnoncontradiction. The fallacy applies only to objective facts, or what are alleged...
satisfies De Morgan's laws) In a De Morgan algebra, the laws ¬x ∨ x = 1 (lawof the excluded middle), and ¬x ∧ x = 0 (lawofnoncontradiction) do not always...
This violates the lawofnoncontradiction and, by extension, bivalence. However, this is only a partial rejection of these laws because P is only partially...
unity of opposites and change, or flux. According to Aristotle, Heraclitus was a dialetheist, or one who denies the lawofnoncontradiction (a lawof thought...
remains a necessary condition for the truth of any argument, owing to the lawofnoncontradiction. The value of a proof largely lies in its ability to reconcile...
consisting of ten chapters each. Each part is named in honor of one of Aristotle's lawsof logic: "Non-Contradiction" after the lawofnoncontradiction; "Either-Or"...
Hook, and his dissertation dealt with the metaphysical status of the lawofnoncontradiction. He taught philosophy for many years at various colleges. Peikoff...
Properties of classical logics: Lawof the excluded middle Double negation elimination Lawofnoncontradiction Principle of explosion Monotonicity of entailment...
never be true and false at the same time (lawofnoncontradiction) and they must be at least true or false (lawof excluded middle). The Stoics catalogued...
(1912:74) lists three lawsof thought that derive from Aristotle: (1) The lawof identity: "Whatever is, is.", (2) The lawofnoncontradiction: "Nothing can both...
schema. As of 1999, it could be summarized as follows: Truth about reality is knowable. Opposites cannot both be true (The LawofNoncontradiction). It is...
reasoning. This is since while deductive reasoning is justified by the lawofnoncontradiction, induction lacks this justification. Al-Sadr aims in this book...
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