Shapiro argues that both realist and anti-realist accounts of mathematics are problematic. To resolve this dilemma, he articulates a structuralist approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, butrather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. | Philosophy of Mathematics by Stewart Shapiro, Hardcover | Indigo Chapters