A proposition arrived at by the methods of logical deduction from a set of basic postulates or axioms accepted as primitive and therefore not subject to deductive proof. So long as a theorem is part of a purely formal system, it is not meaningful to speak about the “truth” of a theorem but only about its “correctness.” It becomes true when it, or its consequences, can be shown to be in accord with observable facts. The classic example of a system of theorems is afforded by Euclid's system of geometry, which is now recognized to have only a purely formal character, although it was formerly considered to be meaningful to ask whether Euclid's geometry was “true.”