 Kant had held that both arithmetic and (Euclidean) geometry were synthetic a priori, just as—for him—metaphysics was. Indeed, this was to explain the special status of both mathematics and metaphysics, so that the latter could enjoy the exalted status of the former. For Kant, both mathematics and metaphysics afforded informative insights into the nature of reality (they were synthetic); yet, for all that, the rational intellect needed no sensory experience in order to attain such insights (they were a priori). On Kant’s account, even a simple computational statement of arithmetic—let alone a statement involving quantification over the natural numbers—is synthetic. Here is how he put the matter in his Critique of Pure Reason, at B16: 