Contradictions in logic: threat to mathematics?

Contradictions in logic: threat to mathematics?

In the world of logic and mathematics, contradictions are of central importance, since they form the basis for the correctness of statements. As Spektrum reported the antique philosopher aristoteles ago three fundamental thinking laws, including the "law of Objection ”. This law states that a statement cannot be true and wrong at the same time, which is essential for logic.

contradictions in the logic signal a wrong thought process, while paradoxes, such as the liar paradox, can lead to indefinable contradictions. An example of this is the sentence: "This sentence is wrong", which leads to a logical conflict. Such contradictions are intolerable in the logic, since on the principle of "ex falso quodlibet" they mean that any statements can be derived from an objection. A clear example of this is the derivation of unicorns: the statement "Omar is married or Maria is two meters tall" could lead from a contradiction, to the conclusion that there are unicorns.

contradictions and their problems

The implication that a contradiction could make everything true is considered problematic. Some experts therefore propose the development of a "paracooner" logic to defuse contradictions, but this also entails their own challenges. Another perspective is dialetism, which is accepted and seriously discussed as a real and false statements.

Mathematical logic defines clear rules to avoid contradictions, as these represent the basis of mathematics. Despite intensive discussions and theoretical considerations, a real contradiction in mathematics has so far failed to do so, such as University Siegen determined.

-transmitted by West-Ost-media

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OrtSiegen, Deutschland
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