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Infinity

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Abstract

This essay surveys the different types of infinity that occur in pure and applied mathematics, with emphasis on: 1. the contrast between potential infinity and actual infinity; 2. Cantor's distinction between transfinite sets and absolute infinity; 3. the constructivist view of infinite quantifiers and the meaning of constructive proof; 4. the concept of feasibility and the philosophical problems surrounding feasible arithmetic; 5. Zeno's paradoxes and modern paradoxes of physical infinity involving supertasks.

Publication Date Jan 1, 2007
Publicly Available Date Mar 29, 2024
Pages 523 -585
Book Title Philosophy of Logic, vol. 5 of the Handbook of the Philosophy of Science
ISBN 0-444-51541-0
Keywords actual infinity, potential infinity, transfinite set theory, Cantor, constructivism, intuitionism, proof, feasibility, physical infinity, Zeno's paradoxes, supertasks

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