  As these quotations show, Weyl had come to accept that it was in  principle impossible to furnish the continuum as presented to  intuition with an exact mathematical formulation : so, with  reluctance, he lowered his sights. In Das Kontinuum his goal was, first and foremost, to establish the consistency of the mathematical theory of the continuum by putting the  arithmetical notion of real number on a firm logical basis.  Once this had been achieved, he would then proceed to show that this  theory is reasonable by employing it as the foundation for a plausible account of continuous process in the objective physical   world.[15] 