Tait argues that Kant did not restrict the notion of number or the operations of arithmetic to the natural numbers, but rather, applies the notions of number and arithmetic to geometric magnitudes as well; this results, he says, in a notion that anticipates our modern conception of real numbers. Tait supports this amalgamated reading both historically and textually. Moreover, he takes this insight further, to a sweeping account of Kant’s view of mathematical epistemology, methodology, and metaphysics. In particular, he suggests that, the "pure intuitions," which are so crucial to Kant’s notion of construction, give us what we today may call "generic objects"; and he uses this to explain the a priori applicability of mathematics. Tait then concludes by relating this account of Kant to post-Kantian views of mathematics including his own analysis of the Hilbert–Bernays finitist program in the foundations of mathematics.