Tautology

Definition: A proposition that is necessarily true in all possible circumstances, independent of external facts.

• 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.

• 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 or Petitio principii.

• 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.

• Circular reasoning – 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)?

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.

Input: “Brexit means Brexit.”
Output: This is a circular definition that is semantically vacuous. Flag as tautology.

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