Antynomia

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Antinomial (antinomy) - logical contradiction, paradox, logical sentence, or deductive reasoning that leads to contradiction. Term used in logic, epistemology.

Example: antinomial self-healing.

Is the statement: P = "The proposition P belongs to set A" belongs to set A or not? Otherwise: can the sentence P speak for itself? If so, then sentence P declares that it belongs to set A, ie it declares something about itself, which it can not do as part of set A.

If not, the sentence should belong to the set A, but then it can not decide about itself, so it does not belong to the set A.

As you can see, the assumption that an antinomy is true leads to paradox and at the same time assumes the opposite. Another example of antinomy is the paradox of a liar: "If a liar says he's lying, it means he's always lying and not lying at the same time" (Eubulides of Miletus)

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