Contradiction

In mathematics and logic, contradictions are indeed considered problematic. A contradiction occurs when a statement and its negation are both true at the same time, which is not possible in classical logic. When a contradiction arises in a logical or mathematical argument, it usually indicates that there is an error or inconsistency in the reasoning or the assumptions made.

Mathematicians and logicians strive to avoid contradictions in their work, as they undermine the validity of the arguments and conclusions drawn from them. Consistency is a fundamental property that a well-defined mathematical or logical system must satisfy to be considered valid and reliable. Contradictions are "verboten" (forbidden) in the sense that they signal an issue that needs to be addressed to maintain the integrity of a system or argument.