Existence Theorem - Constructivist Ideas

Constructivist Ideas

From the other direction there has been considerable clarification of what constructive mathematics is; without the emergence of a 'master theory'. For example according to Errett Bishop's definitions, the continuity of a function (such as sin x) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a promise that can always be kept. One could get another explanation from type theory, in which a proof of an existential statement can come only from a term (which we can see as the computational content).