Demonstrables

Demonstrables are propositions or statements that are capable of being demonstrated, either through logical proof or through empirical evidence. The plural usage emphasizes items that can be shown to be true or false by reasons, arguments, or tests. The term derives from the Latin demonstrare, meaning to point out or show.

In philosophy and logic, demonstrables are propositions that can be established as true within a given framework. They can be a priori, proven through deduction from accepted premises, or a posteriori, supported by empirical observation. The status of a proposition as demonstrable can depend on the chosen axioms, rules of inference, or methodological assumptions. This contrasts with claims that are merely asserted, unverifiable, or underdetermined by available methods.

In mathematics, a demonstrable proposition is one that can be proved from axioms via a valid sequence of logical deductions. Demonstrations are formal arguments that establish truth within a formal system. The set of demonstrables in mathematics is precisely the set of theorems and other proved statements derived from accepted axioms.

In the empirical sciences, demonstrables are hypotheses, laws, or claims that can be tested and supported by repeatable observations and experiments. Demonstrability here depends on measurement, instrumentation, and consensus about experimental procedures. Limitations include measurement uncertainty, model dependence, and the potential for future evidence to revise what is considered demonstrable.

Examples often cited include geometric theorems proved from axioms, and experimentally verifiable statements such as physical constants within stated uncertainties.

See also: proof, demonstration, theorem, axiom, hypothesis, falsifiability.