Infinity

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.

Citation

(2007). Infinity. In Philosophy of Logic, vol. 5 of the Handbook of the Philosophy of Science (523 -585)

• Publication Date: Jan 1, 2007
• 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