Mathematics and Its Logics: Philosophical Essays

Geoffrey Hellman argues for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite contradictions between different systems and positing different frameworks serving different purposes. He develops a modal-structuralist account of mathematics, recognizing indefinite extendability of models and stages at which sets occur, and uses extendability to derive axiom of Infinity and Replacement, improve resolutions of set-theoretic paradoxes, and explore advantages and limitations of restrictive systems.

Format: Paperback / softback
Length: 294 pages
Publication date: 10 November 2022
Publisher: Cambridge University Press

Geoffrey Hellman presents a compelling argument for a healthy pluralism in mathematics and its logics, advocating for peaceful coexistence despite apparent contradictions between different systems. He posits diverse frameworks serving distinct legitimate purposes. The essays refine and expand Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory that acknowledges the indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman demonstrates how extendability can be employed to derive the axiom of Infinity and Replacement, improving upon previous accounts. He also showcases how extendability leads to intriguing and novel resolutions of set-theoretic paradoxes. Other essays explore the advantages and limitations of restrictive systems, such as nominalist, predicativist, and constructivist. Additionally, there are two essays, with Solomon Feferman, on predicative foundations of arithmetic.

Geoffrey Hellman presents a compelling argument for a healthy pluralism in mathematics and its logics, advocating for peaceful coexistence despite apparent contradictions between different systems. He posits diverse frameworks serving distinct legitimate purposes. The essays refine and expand Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory that acknowledges the indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman demonstrates how extendability can be employed to derive the axiom of Infinity and Replacement, improving upon previous accounts. He also showcases how extendability leads to intriguing and novel resolutions of set-theoretic paradoxes. Other essays explore the advantages and limitations of restrictive systems, such as nominalist, predicativist, and constructivist. Additionally, there are two essays, with Solomon Feferman, on predicative foundations of arithmetic.

Weight: 438g
Dimension: 151 x 227 x 21 (mm)
ISBN-13: 9781108714006