disproof

Disproof is the act of showing that a claim, proposition, or theory is false or invalid. It entails demonstrating that the statement cannot be correct under its stated conditions, or that its logical consequences are untenable. Disproof is central to logic and critical inquiry, complementing the role of proof.

Methods include presenting a counterexample that falsifies a universal claim; constructing a logical argument that yields a contradiction from the assumption that the claim is true (reductio ad absurdum); and refuting by exposing a flaw in reasoning or evidence. In scientific contexts, disproof often takes the form of falsifying predictions through experiments or observations; in philosophy, it may involve showing that arguments are unsound or that premises are inconsistent.

In mathematics and formal logic, a single counterexample can disprove a universal statement, while proving a statement for some cases does not suffice. Disproof of conjectures can lead to revised hypotheses or domains of applicability rather than a simple negation. Historical examples include the discovery of black swans disproving the claim that all swans are white, and experimental challenges to the luminiferous aether from the Michelson–Morley experiment, which contributed to changes in physical theory.

Limitations include the dependence of disproof on the scope and assumptions of the claim; a disproof in one domain may not transfer to another, and some statements may be undecidable with current methods. Disproof often prompts refinement, revision, or abandonment of ideas rather than a straightforward replacement.

See also: refutation, falsification, counterexample, proof by contradiction.