Five stages of accepting constructive mathematics

Five Stages of Accepting Constructive Mathematics

On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced c...

Constructive Mathematics

Constructive Mathematics , in

The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics (BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin...

Constructive mathematics without choice

What becomes of constructive constructive mathematics without the axiom of (countable) choice? Using illustrations from a variety of areas, it is argued that it becomes better. Despite the apparent unanimity among schools of constructive mathematics with respect to the acceptance of the countable axiom of choice, I believe it to be one of the central problems, or mysteries, of constructive math...

Informal Constructive Reverse Mathematics