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Encyclopedia > Principle of contradiction

The Principle of contradiction (principium contradictionis in Latin) is, in logic, the term applied to the second of the three primary laws of thought. The oldest statement of the law is that contradictory statements cannot both at the same time be true, e.g. the two propositions A is B and A is not B are mutually exclusive. A may be B at one time, and not at another; A may be partly B and partly not B at the same time; but 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 quality. This is the statement of the law given by Aristotle. It takes no account of the truth of either proposition; if one is true, the other is not; one of the two must be true. Latin is an ancient Indo-European language originally spoken in the region around Rome called Latium. ... Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Aristotle, marble copy of bronze by Lysippos. ...


Modern logicians, following Leibnitz and Kant, have generally adopted a different statement, by which the law assumes an essentially different meaning. Their formula is A is not not-A; in other words it is impossible to predicate of a thing a quality which is its contradictory. Unlike Aristotle's law this law deals with the necessary relation between subject and predicate in a single judgment. Whereas Aristotle states that one or other of two contradictory propositions must be false, the Kantian law states that a particular kind of proposition is in itself necessarily false. On the other hand there is a real connection between the two laws. The denial of the statement A is not-A presupposes some knowledge of what A is, i.e. the statement A is A. In other words a judgment about A is implied. Leibnitz town hall with Mariensäule Leibnitz is a city in Styria, Austria and, as of 2001, has about 6892 inhabitants. ... Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ...


Kant's analytical propositions depend on presupposed concepts which are the same for all people. His statement, regarded as a logical principle purely and apart from material facts, does not therefore amount to more than that of Aristotle, which deals simply with the significance of negation.


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LUKASIEWICZ ON THE PRINCIPLE OF CONTRADICTION (10449 words)
Since the principle of contradiction occupies a position in logic analogous to that of the parallel line postulate in Euclidean geometry, a revision of the principle of contradiction becomes necessary, that is, a revision of the basis of Aristotelian logic in the light of the latest results of symbolic logic.
The former concerns the conception of a non-Aristotelian logic, that is, a logic operating without the principle of contradiction, a natural consequence of the asserted independence of the principle of the syllogism from the principle of contradiction (3).
The principle of identity ("to each object belongs that characteristic to which it belongs"), for example, could be considered as one of these principles since it does not need, unlike the principle of contradiction, negation and logical multiplication.
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