PREFACE -- Contents -- 1. Realism -- 1. Pre-theoretic realism -- 2. Realism in philosophy -- 3. Realism and truth -- 4. Realism in mathematics -- 2. Perception and Intuition -- 1. What is the question? -- 2. Perception -- 3. Intuition -- 4. Gödelian Platonism -- 3. Numbers -- 1. What numbers could not be -- 2. Numbers as properties -- 3. Frege numbers -- 4. Axioms -- 1. Reals and sets of reals -- 2. Axiomatization -- 3. Open problems -- 4. Competing theories -- 5. The challenge -- 5. Monism and Beyond -- 1. Monism -- 2. Field's nominalism -- 3. Structuralism -- 4. Summary -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.