 Such a game formalist is a more worthy opponent for the platonistic Frege to tackle, but there are two main objections he sets out which still apply to this more sophisticated position. The first is the question of applicability: if mathematics is just a calculus in which we shuffle uninterpreted symbols (or symbols whose interpretation is a matter of no importance), then why has it been applied so successfully—and in so many ways, to so many different things—ordinary physical objects, sub-atomic objects, fields, properties, and indeed from one part of mathematics to another (we can count the number of dimensions in a pure geometric space)? Frege writes: