Between Galois connections and (some metamathematical) solutions of equations fgf=f and gfg=g Original Research Article

The method based on the idea of Galois connection is well known. It facilitates investigations into similarities between mathematical structures, including isomorphisms between these structures, the highest degree of similarity. This idea is employed here and adapted so as to get to the core of aspects of the relationship between some metamathematical structures. The focus is put on the relation between traditional methodological orthodoxy based on the idea of proof (polished up with the help of the concept of closure operator), on the one hand, and on some alternative methodological set-ups based on other ideas such as consistency or some forms of maximality, on the other hand.