A standard picture of the conception of a priori knowledge developed within the logical empiricist tradition runs as follows. This conception arose primarily in the context of the philosophy of mathematics - where, in particular, it was intended to provide an alternative to the Kantian theory of synthetic a priori knowledge that would be both acceptable from an empiricist point of view and more adequate to mathematical practice than the simple-minded empiricism associated with John Stuart Mill. Here the logical empiricists found an answer in the logicist philosophy of mathematics of Gottlob Frege and Bertrand Russell, according to which mathematics is reducible to logic (the new mathematical logic developed by Frege and Russell) and is therefore analytic a priori, not synthetic a priori. There is thus no need of the Kantian faculty of pure intuition, and, at the same time, we can still (thanks to the richness and complexity of Frege's and Russell's new logic) do justice to both the a priority and the complexity of our actual mathematical knowledge. The heart of the logical empiricists' answer to Kant, therefore, is that his main example of synthetic a priori knowledge, pure mathematics, is not synthetic after all. All that we ultimately need to explain the possibility of pure a priori knowledge in the exact sciences is the analytic a priori.