Law of noncontradiction

The principle of contradiction or law of contradiction states that two contradictory statements can not be true at the same time. Over the philosophy and history of science and of different theoretical positions of the sentence was based on opposition to different types of contrasts and has been understood in different ways as an ontological, epistemological or logical principle.

The principle of contradiction is to be distinguished from the law of excluded middle and the principle of bivalence.

Logic

In logic, the law of contradiction often, always, based on a sentence and its negation set in modern formal logic. This implies the proposition that a statement at the same time ( their sentence negation ) can not meet with their opposite. It is therefore not possible, for example, at the same time the soil is a disk and that it is not the case that the ground is flat.

In SL, this rate is determined by the formula

Expressed.

The principle of contradiction is a fundamental principle of classical logic.

In many non-classical logical systems, this set is accepted and can be derived. However, there are logical systems in which the sentence is not true of the opposition.

Philosophy

In philosophy, the principle of contradiction (also principle of contradiction or non - contradiction principle called ) one of the most important statements of epistemology and the traditional logic, where he is regarded as one of the laws of thought; partly it is also regarded as an ontological principle. Aristotle formulated in his Metaphysics:

" But the surest principle of all is the one in which a delusion is impossible [ ... ] Which is but, we now want to specify: For it is impossible that the same same same relation also zukomme and does not accrue. [ ... ] However, we have just assumed that it was impossible that something is at the same time and was not. "

Theology

In the encyclical Fides et Ratio, Pope John Paul II the principle of contradiction is calculated under the name " principle of non-contradiction " to the core philosophical insights that are always present in the history of thought. This core imagine such a thing as a spiritual heritage of mankind dar. These core components of an "implicit philosophy " would - although possibly in indistinct, unreflective form - shared by all and should, in the opinion of the Pope represent a reference point for the different philosophical schools.

Discussion of the sentence

The principle of contradiction is - particularly by the realists - counted as evidence. These are the first truths or fundamental truths on which to build all other truths or implied, by any other single truth. On the principle of contradiction, the unprovable and irrefutable evidence of is particularly pronounced. Any attempt to prove it or disprove would always presuppose it, because every statement and every argument yes and not intended to convey its opposite.

Also for the analytical judgments in Immanuel Kant the principle of contradiction applies. The statement: " A body is extended " is " analytically ", because the concept of extension is already included in the concept of the body. The analytical knowledge is a pure analysis of findings or concepts. In contrast, there are synthetic judgments in which the content of a concept or knowledge is extended, eg: ". The body is red" Again, however, without prejudice to the principle of contradiction, because the body at the same time and in the same relationship is not red and not is red. The analytical truth is ultimately grounded in the principle of contradiction (Ernst Tugendhat ).

In contrast to the law of excluded middle, the principle of contradiction in intuitionistic logic applies. But the sentence is not to discriminate paraconsistent logics, since they are often not completely agnostic to contradictions in general.

Georg Wilhelm Friedrich Hegel tried to (in the sense of a theory of opposites in things ) enforce the member for whom he dialectics to extend the logic in a way (so-called dialectical logic), which sets the principle of contradiction except validity. Thus, Hegel tried to circumvent Kant's refutation of the so-called ' dogmatism of metaphysics '. The philosopher of science Karl Popper commented: "This refutation [ Kant ] Hegel regarded as valid only for systems that are metaphysical in its narrowest sense, it is not required for the dialectical rationalism, which takes into account the development of reason and therefore not to fear contradictions. By Hegel avoids the Kantian criticism in this way, he throws himself into a very dangerous adventure that must lead to disaster; because he argues like this:, Kant refuted rationalism by saying that it must lead to contradictions. This I admit. But it is clear that this argument derives its strength from the law of contradiction: it refuted only those systems that accept this law, ie, those who intend to be free of contradictions. The argument is not dangerous for a system like mine that is willing to accept contradictions - ie. of a dialectical system ' There is no doubt that Hegel's argument erects a dogmatism of an extremely dangerous kind - a dogmatism that needs to fear no more attack [see immunization strategy ]. For any attack, any criticism of any theory must be based on the method, show any contradictions, either in a theory itself or between a theory and some facts [ ... ]. "