Sophism is an inference or reasoning that substantiates some known incongruity, absurdity, or paradoxical statement contradicting generally accepted notions. The initial persuasiveness of many sophisms (their 'logical' character) is usually related to a well-concealed error on the semiotic or logical level. Errors on the semiotic level usually involve metaphorical speech, homonymy and polysemy, and amphibology, which violate the unambiguous character of the thought and lead to a confusion of the meanings of terms. Errors on the logical level include deceptive substitution of the basic thought (thesis of the proof), the taking of false premises for true ones, violation of the permissible methods of reasoning, and the use of 'unauthorized' or 'forbidden' rules or actions, such as division by zero in a mathematical sophism.