ABSTRACT
Reacting against the prevalence of nonconstructive proofs in analysis, Kronecker emphasized the desirability of using con structive methods of proof long before the discovery of paradoxes in set theory. The problem of constructive proofs continues today to enjoy a fair amount of attention. Not only can Brouwer’s position be regarded as a call to banish nonconstructive proofs but even Hilbert’s approach can also be regarded as a request to justify nonconstructive proofs by constructive methods. And there are recent attempts to develop constructive mathematics. In mathematical logic we have quite a bit of work on the nature and peculiarities of constructive proofs. For example, working mathematicians often have a pretty good idea how certain nonconstructive proofs can be transformed into constructive ones. Mathematical logic makes pos sible a more explicit and more systematic treatment of large classes of proofs on which such transformations can be made.
