Books by Stewart (Professor of Philosophy Shapiro

Stewart Shapiro presents a distinctive original view of the foundations of mathematics, arguing that second-order logic has a central role to play in laying these foundations. He gives an accessible account of second-order and higher-order logic, paying special attention to philosophical and historical issues.

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.

'Thinking about Mathematics' covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill.