Mathematics Without Numbers: Towards a Modal-Structural Interpretation

This book develops a comprehensive alternative to standard Platonism as an approach to fundamental issues in the philosophy of mathematics. It works out a detailed interpretation of mathematics as the investigation of structural possibilities rather than referring to absolute, Platonic objects. After dealing with natural numbers and analysis, the approach is extended to set theory, where it is shown how to dispense with a fixed universe of sets. The final portion of the book is devoted...
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This book develops a comprehensive alternative to standard Platonism as an approach to fundamental issues in the philosophy of mathematics. It works out a detailed interpretation of mathematics as the investigation of structural possibilities rather than referring to absolute, Platonic objects. After dealing with natural numbers and analysis, the approach is extended to set theory, where it is shown how to dispense with a fixed universe of sets. The final portion of the book is devoted to the topic of applied mathematics, and the problems involved in applying the work to the physical world.