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The essays in this volume present a case for pluralism in mathematics and its logics, largely supporting coexistence despite apparent contradictions between different systems. In addition, the volume further develops Hellman's modal-structuralist account of mathematics, recognizing indefinite extendability of models and stages at which sets occur.

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This study of mathematical structuralism explores its core concern with interrelations in abstraction from the nature of objects.

Hellman here presents a detailed interpretation of mathematics as the investigation of "structural possibilities, " as opposed to absolute, Platonic objects. After treating the natural numbers and analysis, he extends the approach to set theory, where he demonstrates how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.

Offers both a new account of the continuous and a historical study of the development of our understanding of the notion~Draws together philosophy and mathematics in a way that is accessible to non-specialist readers~Co-authored by two eminent philosophers

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