  However, there may of course be logical relations between the two views. Given the origin of working realism, it is not surprising that the view receives strong support from mathematical platonism. Assume that mathematical platonism is true. Then clearly the language of mathematics ought to be as described in (i). Secondly, provided it is legitimate to reason classically about any independently existing part of reality, (ii) would also follow. Thirdly, since platonism ensures that mathematics is discovered rather than invented, there would be no need for mathematicians to restrict themselves to constructive methods and axioms, which establishes (iii). Fourth, there is a powerful and influential argument due to Gödel (1944) that impredicative definitions are legitimate whenever the objects being defined exist independently of our definitions. (For instance, ‘the tallest boy in the class’ appears unproblematic despite being impredicative.)  If this is correct, then (iv) would follow. Finally, if mathematics is about some independently existing reality, then every mathematical problem has a unique and determinate answer, which provides at least some motivation for Hilbertian optimism. (See, however, the discussion of plenitudinous platonism in Section  4.2.)