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).
Read more about this topic: Existence Theorem
Famous quotes containing the word ideas:
“Our ideas are the offspring of our senses; we are not more able to create the form of a being we have not seen, without retrospect to one we know, than we are able to create a new sense. He whose fancy has conceived an idea of the most beautiful form must have composed it from actual existence.”
—Henry Fuseli (1741–1825)