demonstrabile

Demonstrabile is an adjective that describes something that can be demonstrated or proven. In Italian, it translates roughly as provable or demonstrable in English, and is used in mathematics, logic, science, and everyday language. The term derives from Latin demonstrabilis, from demonstrare, to show or point out.

In mathematics and logic, a proposition is demonstrabile if there exists a proof within a given formal system. Demonstrability is tied to the notion of provability: something may be demonstrabile within a theory, but not necessarily true in an absolute sense. Gödel’s incompleteness theorems show that in any sufficiently powerful formal system, there are true statements that are not demonstrable within that system.

In empirical science, demonstration requires evidence that is reproducible and observable. A claim is considered demonstrable when experiments or observations reliably support it, and when independent researchers can reproduce the results. Demonstrability, in this sense, is provisional and subject to revision in light of new data.

In philosophy and rhetoric, the term is used to describe claims that can be argued to be true on the basis of reason or experience, rather than merely asserted. The strength of a demonstrabile claim depends on the robustness and coherence of the supporting argument and evidence.

See also: proof, theorem, evidence.