selfrefutation

Self-refutation, sometimes written as selfrefutation, refers to a statement, argument, or theory that would undermine itself if accepted as true or valid. In its core, a self-refuting claim is one whose very truth would contradict its claim, thereby defeating its own purpose or credibility.

A classic example is the liar paradox: "This sentence is false." If the sentence is true, then it is false, and if it is false, then it is true. Such self-referential constructions expose problems in how language and truth conditions are defined. Other examples include general self-referential claims like "All my statements are lies," or arguments that rely on an assumption that cannot consistently hold without refuting themselves.

Self-refutation is a major concern in philosophy, logic, and semantics because it highlights the limits of truth, reference, and formal reasoning. It is closely connected to semantic paradoxes, including the Liar Paradox and related self-reference problems, and it motivates investigations into how languages can represent truth without collapsing into inconsistency.

Responses to self-refutation vary. Some approaches seek to avoid paradox by using hierarchical or stratified theories of truth (to separate levels of discourse) or by developing formal logics such as paraconsistent logics, which tolerate some contradictions without explosion. Others appeal to context, vagueness, or alternative semantics to assign meaningful evaluations to self-referential statements.

In practice, self-refutation can function as a diagnostic tool in critique, revealing hidden assumptions or the fragility of arguments. It also informs discussions about the foundations of logic, mathematics, and language.