chapter  4
31 Pages

Mathematical thinking

Platonism, according to one unsympathetic commentator, ‘assimilates mathematical enquiry to the investigations of the astronomer: mathematical structures, like galaxies, exist independently of us, in a realm of reality which we do not inhabit but which those of us who have the skill are capable of observing and reporting on’ (Dummett 1973, 229). I’ll call this view of mathematics ‘π in the sky’—but not scornfully, though perhaps with a touch of self-mockery, since I think it is true. Mathematics is best accounted for by appeal to real Platonic entities; not only do they provide the grounds for mathematical truth, but these abstract objects are also somehow or other responsible for our mathematical intuitions and insights.