> But however this may work as a classification, it isn't the structure > that I'm looking for. Foundations (math. logic, set theory, etc.) > couldn't possibly be a branch at the same level as these others. And a > <snip> > This is really an old-fashioned project. I had assumed that there must > have been some systematizers who had worked on this, even if one had to > go back a bit in time to find them. >
Maybe you will find (the start of) what you're looking for in Whitehead & Russell "Principia Mathematica" which attempted to derive mathematics from logic; or Bourbaki "Elements of Mathematics", see the "Contents of The Elements of Mathematics Series" at the start of any of the many volumes.