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.
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.
However, it is impossible to predicate of the same thing, at the same time, and in the same sense, the absence and the presence of the same fixed quality.
The Buddhist Tripitaka attributes to Nigaṇṭha Nātaputta, who lived in the 6th century BCE, the implicit formulation of the law of noncontradiction, “‘See how upright, honest and sincere Citta, the householder, is’; and, a little later, he also says: ‘See how Citta, the householder, is not upright, honest or sincere.’ To this, Citta replies: ‘if your former statement is true, your latter statement is false and if your latter statement is true, your former statement is false.’” Early explicit formulations of the law of noncontradiction were ontic, with later 2nd century Buddhist philosopher Nagarjuna stating “when something is a single thing, it cannot be both existent and non-existent” similar to Aristotle’s own ontic formulation that “that a thing cannot at the same time be and not be”.
Parmenides employed an ontological version of the law of non-contradiction to prove that being is and to deny the void, change, and motion.
nor could you point it out... For the same thing is for thinking and for beingThe nature of the 'is' or what-is in Parmenides is a highly contentious subject.
[7] In Plato's early dialogues, Socrates uses the elenctic method to investigate the nature or definition of ethical concepts such as justice or virtue.
In this, Plato carefully phrases three axiomatic restrictions on action or reaction: in the same part, in the same relation, at the same time.
Rather than starting with experience, Aristotle begins a priori with the law of non-contradiction as the fundamental axiom of an analytic philosophical system.
Now, he starts with much stronger logical foundations than Plato's non-contrariety of action in reaction to conflicting demands from the three parts of the soul.
[20][21] Leibniz and Kant both used the law of non-contradiction to define the difference between analytic and synthetic propositions.
[22] For Leibniz, analytic statements follow from the law of non-contradiction, and synthetic ones from the principle of sufficient reason.
The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as: Graham Priest advocates the view that under some conditions, some statements can be both true and false simultaneously, or may be true and false at different times.
[28][29] Some, such as David Lewis, have objected to paraconsistent logic on the ground that it is simply impossible for a statement and its negation to be jointly true.
[31][full citation needed][32][full citation needed] Those who (like the dialetheists) claim that the Law of Non-Contradiction can be violated are in fact using a different definition of negation, and therefore talking about something else other than the Law of Non-Contradiction which is based on a particular definition of negation and therefore cannot be violated.
For example, she is still the acting chief of police while having been demoted from the position, and tries to investigate a man that both was and was not named Ennis Stussy, and who both was and was not her stepfather.