Philosophers before Kant assumed that all a priori (non-empirical) judgments must be analytic, and also that all synthetic judgments must be a posteriori (empirical). Applied to the classical example of the axioms of geometry, these assumptions produced two opposing schools of thought—some philosophers said that geometry had to be empirical because its axioms were obviously synthetic; the other said that geometry had to be analytic because its axioms were obviously a priori. Kant's discovery that the two distinctions were not identical allowed for a middle ground position in which the axioms of geometry (as well as many other propositions) had to be synthetic a priori.