What do we call a statement that can be proved through logical reasoning and accepted principles?

The term that refers to a statement that can be proved through logical reasoning and accepted principles is a theorem. In mathematics and logic, a theorem is a formal statement that has been rigorously proven based on previously established statements such as other theorems, axioms, and postulates. The process of proving a theorem typically involves deductive reasoning and follows logically from accepted premises.

To clarify the other terms, a hypothesis is an initial conjecture or educated guess that requires testing and validation, but it is not necessarily proven. A postulate is an assumption or self-evident truth that is accepted without proof, serving as a foundation for proving other statements. An axiom is similar to a postulate, representing a fundamental principle that is taken for granted within a given system. Understanding these distinctions helps highlight why a theorem is specifically defined by its proven nature.