Mathematics and Its Logics

Philosophical Essays

Geoffrey Hellman (University of Minnesota)

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English

Cambridge University Press
04 February 2021

Philosophy: logic; Philosophy of mathematics; Mathematical logic

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.

By: Geoffrey Hellman (University of Minnesota)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 158mm, Spine: 22mm
Weight: 590g
ISBN: 9781108494182
ISBN 10: 1108494188
Pages: 288
Publication Date: 04 February 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Geoffrey Hellman is Professor of Philosophy at the University of Minnesota, Twin Cities. His publications include Mathematics without Numbers: Towards a Modal-Structural Interpretation (1989), Varieties of Continua: From Regions to Points and Back (with Stewart Shapiro, 2018), and Mathematical Structuralism, Cambridge Elements in Philosophy of Mathematics (with Stewart Shapiro, Cambridge, 2018).