 Carnap had not only studied with Frege, but like many of the logical empiricists he had started out as a neo-Kantian as well. So especially in view of Russell’s relatively more successful attempt at reducing mathematics to logic, it was perhaps natural that Carnap would consider both mathematics and logic as analytic. Geometry could be handled in several different ways that we will not discuss here. But from fairly early on there was widespread agreement among the logical empiricists that there was no synthetic a priori, and that logic and mathematics and perhaps much else that seemed impervious to empirical disconfirmation should be thought of as analytic. The point of drawing the analytic-synthetic distinction, then, is not to divide the body of scientific truths or to divide philosophy from science, but to show how to integrate them into a natural scientific whole. Along the way the distinction clarifies which inferences are to be taken as legitimate and which are not. If, as Carnap and Neurath were, you are impressed by Duhemian arguments to the effect that generally claims must be combined in order to test them, the analytic-synthetic distinction allows you to clarify which combinations of claims are testable.