HUSSERL AND HILBERT ON COMPLETENESS

Only in this sense of the impossibility of a proper representation of an infinite set is it correct to say: there is no actual infinite.13After this interruption Weyl comes eventually to the third and last level of Husserls phenomenological approach to mathematics: Because we are compelled by other irrefutable reasons to introduce infinite sets indeed analysis alone forces this when finally we come to the third level, where we erect the theory of finite and infinite sets and numbers in a scientifically systematic way by setting up appropriate axioms, definitions and the consequences drawn from them. [...]we have to expand the Urdomain by a set of new elements, which enable us to perform the operation, let us say, of subtraction or division unlimited. [...]one cannot judge whether the axiomatic characterization of the Urdomain is complete. [...]the above statement is only correct if we take the entire set of natural numbers as the Urdomain.