Mathematical activity doesn't proceed from axioms. Axioms proceed from mathematical activity. The philosophy that grew out of the axiomatization of mathematics

Mathematical activity doesn't proceed from axioms. Axioms proceed from mathematical activity. The philosophy that grew out of the axiomatization of mathematics in the early 20th century never really took root in its culture or practice. If you want to read a philosophical account of mathematics as it is actively practiced today, Synthetic Philosophy of Contemporary Mathematics by Zalamea (a practicing mathematician) is good. It is far more sympathetic to postmodernism than you would think. And for an account of modern logic by a logician in a postmodern vein, La Fantome de la Transparence by Girard is gr8. Only in French atm.