dimostrabile

Dimostrabile is an Italian adjective meaning that something can be demonstrated, proven, or shown to be true through argument, calculation, or evidence. The form derives from dimostrare (to demonstrate or prove) and is used across mathematics, logic, philosophy, and everyday language. The noun dimostrazione refers to the act of proving, while dimostrabilità (or demonstrabilità) denotes the quality of being demonstrable.

In mathematics and formal logic, a proposition is considered dimostrabile if there exists a formal proof of its truth from a given set of axioms. Demonstrability is relative to the chosen axiomatic system; a statement may be dimostrabile within one framework and not within another. Gödel's incompleteness theorems illustrate limits to dimostrabilità in sufficiently strong, consistent systems: some true statements cannot be proved inside the system.

In empirical sciences, a hypothesis or claim is described as dimostrabile when it can be supported by observable evidence, experiments, or measurements, and when such support can be independently checked. There, demonstrability is provisional and depends on methods and data; not all true claims are currently dimostrabile with available techniques.

In everyday usage, dimostrabile conveys that a fact or assertion has been established with justification or proof. The term is often contrasted with indimostrabile (undemonstrable) or non-dimostrabile, used for claims lacking adequate proof or verifiability, as well as with verifiable or testable statements in scientific discourse.

Related concepts include dimostrazione, dimostrabilità, and indimostrabile.