Philosophy of Mathematics

A structuralist approach to mathematical theory in which Shapiro argues that both realist and anti-realist accounts of mathematics are problematic . He claims that mathematical theory is not a fixed domain of numbers that exist independent of one another, but a natural structure with an initial object and successor relation.

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Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout its history and covers historical figures, such as Plato, Aristotle, Kant, and Mill. It presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.