 Unlike the intuitionists, Hilbert was not prepared to take a revisionist stance toward the existing body of mathematical knowledge. Instead, he adopted an instrumentalist stance with respect to higher mathematics. He thought that higher mathematics is no more than a formal game. The statements of higher-order mathematics are uninterpreted strings of symbols. Proving such statements is no more than a game in which symbols are manipulated according to fixed rules. The point of the ‘game of higher mathematics’ consists, in Hilbert’s view, in proving statements of elementary arithmetic, which do have a direct interpretation (Hilbert 1925).