  Nevertheless, Weyl felt that this fact, inescapable as it might be,  could not justify extending the bounds of mathematics to embrace  notions, such as the actual infinite, which cannot be given fully in  intuition even in principle. He held, rather, that such extensions of mathematics into the transcendent are warranted only by the fact that mathematics plays an indispensable role in the physical sciences, in  which intuitive evidence is necessarily transcended. As he says in  The Open   World[8]:  