Understanding the Infinite

Bibliographic Data

ID10693040
AuthorsStewart Shapiro (0000-0002-4895-0772), Mary Ellen Smircich, Shaughan Lavine
Year1996
Volume105
Issue2
Pages256
Publication date1996-04-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueThe Philosophical Review (JOURNAL)
Journal identifiersISSN: 0031-8108 • E-ISSN: 1558-1470
PublisherJSTOR (PUBLISHER)
DOI10.2307/2185727
OpenAlexW2032723756
LanguageEN
Citations received13

Part 1 Introduction. Part 2 Infinity, mathematics' persistent suitor: incommensurable lengths, irrational numbers Newton and Leibniz go forward, and faith will come to you vibrating strings infinity spurned infinity embraced. Part 3 Sets of points: infinite sizes infinite orders integration absolute versus transfinite paradoxes. Part 4 What are sets?: Russell Cantor appendix A - letter from Cantor to Jourdain, 9 July 1904 appendix B - on an elementary question of set theory. Part 5 The axiomatization of set theory: the axiom of choice the axiom of replacement definiteness and Skolem's paradox Zermelo go forward, and faith will come to you. Part 6 Knowing the infinite: what do we know? what can we know? getting from here to there. Part 7 Leaps of faith: intuition physics modality second-order logic. Part 8 From here to infinity: who needs self-evidence? picturing the infinite the finite mathematics of indefinitely large size the theory of zillions. Part 9 Extrapolations: natural models many models one model or many? sets and classes natural axioms second thoughts schematic and generalizable variables

Analytic philosophy · Contemporary philosophy · Epistemology · General interest · Computability, Logic, AI Algorithms · Philosophy · Philosophy and Theoretical Science

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