Description
The author argues that there is a dilemma in the philosophy of mathematics between realism and anti-realism. He then articulates a structuralist approach to resolving the dilemma, which argues that the subject matter of a mathematical theory is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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