Realism in mathematics

Realism: Pre-theoretic realism Realism in philosophy Realism and truth Realism in mathematics Perception and intuition: What is the question? Perception Intuition Godelian Platonism Numbers: What numbers could not be Numbers as properties Frege numbers Axioms: Reals and sets of reals Axiomization Open problems Competing theories The challenge Monism and beyond: Monism Field's nominalism Structuralism Summary References Index.