  Weyl points out that, just as in theoretical physics, Hilbert’s  account of mathematics “already… goes beyond the bounds  of intuitively ascertainable states of affairs through… ideal  assumptions.” (Weyl 1927, 484.) If Hilbert’s realm of  contentual or “real” propositions—the domain of  metamathematics—corresponds to that part of the world directly  accessible to what Weyl terms “insight” or  “phenomenal knowledge”, then “serious”  mathematics—the mathematics that practicing mathematicians are  actually engaged in doing—corresponds to Hilbert’s realm of  “ideal” propositions. Weyl regarded this realm as the  counterpart of the domain generated by “symbolic  construction”, the transcendent world focussed on by  theoretical physics. Hence his memorable characterization: