As in the moral case, non-naturalist realism faces epistemological challenges, to which one response is to posit a faculty of intuition which gives us access to the abstract mathematical realm.  Kurt Gödel arguably favoured a view along these lines (Parsons 1995). However, once more this only seems to push the problem back.  There seems no good way for the posited faculty to bridge the causal gap between the abstract and the spatiotemporal realms without generating implausible overdetermination.