Back مبدأ عدم التناقض Arabic Principi de no contradicció Catalan یاسای ناتەبایی CKB Zásada sporu Czech Kontradiktionsprincippet Danish Satz vom Widerspruch German Principo de nekontraŭdiro Esperanto Principio de no contradicción Spanish اصل امتناع تناقض Persian Principe de non-contradiction French
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 "the house is white" and "the house is not white" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). For example it is tautologous to say "the house is not both white and not white" since this results from putting "the house is white" in that formula, yielding "not (the house is white and not (the house is white))", then rewriting this in natural English. The law is not to be confused with the law of excluded middle which states that at least one of two propositions like "the house is white" and "the house is not white" 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 a so-called logical space, the points in which are all the consistent combinations of propositions. Each combination would contain exactly one member of each pair of contradictory propositions, so the space would have two parts which 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.