Beweisbare

Beweisbare is a German adjective meaning provable or demonstrable. It describes statements, propositions, or claims that can be shown to be true by proof or by adequate evidence within a specified framework. The term is often used in mathematics, logic, philosophy, and to some extent in scientific discourse.

In mathematics and formal logic, a statement is beweisbar if there exists a formal proof from a given set of axioms using accepted rules of inference. A proof consists of a finite sequence of justified steps that leads from axioms and definitions to the statement. Beweisbarkeit is therefore relative to the chosen axioms; a statement may be beweisbar in one system and not beweisbar in another. Gödel’s incompleteness theorem highlights that in any sufficiently strong formal system there are true statements that are not beweisbar within that system.

In science, beweisbar often corresponds to empirical support. Scientific claims are typically described as belegt or supported rather than absolutely proven in a mathematical sense, because evidence can be contingent, probabilistic, or open to revision. Philosophical discussions may distinguish between what is beweisbar and what is true, examining limitations of formal justification and the role of evidence.

Beweisbarkeit is the noun form referring to the property of being provable. The related term unbeweisbar denotes the opposite, meaning not provable within the given framework. The concept underpins debates about proof, truth, and evidence across disciplines.