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Mathematics and Its Logics - Philosophical Essays (Hardcover)
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Mathematics and Its Logics - Philosophical Essays (Hardcover)
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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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