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  3. Mathematics and Its Logics
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    • Publisher:
      Cambridge University Press
      Publication date:
      26 January 2021
      04 February 2021
      ISBN:
      9781108657419
      9781108494182
      9781108714006
      DOI:
      https://doi.org/10.1017/9781108657419
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.59kg, 296 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.44kg, 296 Pages
      • Subjects:
      Mathematics, Logic, Categories and Sets, Philosophy of Science, Philosophy
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    Subjects:
    Mathematics, Logic, Categories and Sets, Philosophy of Science, Philosophy
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    Book description

    In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.

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