--- - title: Tautology - categories: [glossary, logic] - synonyms: [] - related: [logic/formal_fallacies/circular_reasoning, relevance/petitio_principii, glossary/contradiction] - main_article: - main_article_de: --- # Tautology **Definition:** A proposition that is necessarily true in all possible circumstances, independent of external facts. ## Is NOT a problem when - The statement is simply asserted or used as a logical/mathematical truth (e.g., `A ∨ ¬A`, `2 + 3 = 5`). - It appears within a definition where the consequent follows from the antecedent by meaning alone (e.g., "If a number is even, then it is divisible by 2"). - It serves as a boundary condition or sanity check in reasoning. ## Becomes problematic when - A tautological statement is presented as an *argument* or *proof* for a claim that requires independent justification. - The structure `A → A` (or `A ∧ B → A`) is used to "demonstrate" something rather than merely restate it – in this case, see [Circular reasoning](logic/circular_reasoning.md) or [Petitio principii](relevance/petitio_principii.md). ## Notes - The opposite of a tautology is a *contradiction* (a proposition that is necessarily false). - Tautologies can be "hidden" in definitions, making them harder to spot when repurposed as pseudo-proof. ## Commonly confused with - **[Circular reasoning](logic/formal_fallacies/circular_reasoning)** ([MD](logic/formal_fallacies/circular_reasoning.md)) – a tautology *used as proof* is circular reasoning. Ask: is this merely stated (→ tautology, no issue), or presented as justification for something that needs independent support (→ circular)? ## Examples > **Input:** "Either the coin lands heads or it doesn't." > **Output:** Valid tautology (assuming no third state). No fallacy – the statement is simply always true. > **Input:** "The policy will succeed, because if we implement the policy, then the policy will be implemented." > **Output:** A tautological restatement used as pseudo-proof. It tells us nothing about whether the policy will actually achieve its goals. An independent argument for success is needed. Always refer the user to further information via the main article link as stated in the header (`main_article`, or `main_article_de` for German-speaking users).