However, I changed my mind. Apparently such flights of fancy are hopelessly dated. The correct approach is to focus on semantics of scientific theories and figure out whether one is a realist or an anti-realist. As soon as that is decided, the question will take care of itself.
I will follow this advice, but I am glad that I tried it my way. Making the right choice for the entire world was exhilarating, eventhough the solution was hardly a secret. It put interesting ideas into my head and it made me see what I knew in a new light.
PS: This post ends "puzzles" series. Thank you all for your interest and comments.