Coverart for item
The Resource Approaching infinity, Michael Huemer

Approaching infinity, Michael Huemer

Label
Approaching infinity
Title
Approaching infinity
Statement of responsibility
Michael Huemer
Creator
Author
Subject
Language
eng
Summary
Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes. -- Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorDate
1969-
http://library.link/vocab/creatorName
Huemer, Michael
Illustrations
illustrations
Index
index present
LC call number
BD411
LC item number
.H84 2016
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
Infinite
Label
Approaching infinity, Michael Huemer
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover ; Half-Title ; Title ; Copyright ; Dedication ; Contents ; List of Figures; Preface; Part I The Need for a Theory of Infinity; 1 The Prevalence of the Infinite; 1.1 The concept of infinity and the infinite; 1.2 The infinite in mathematics; 1.3 The infinite in philosophy; 1.4 The infinite in the physical world; 1.5 The infinite in modern physics; 1.6 Controversies; 2 Six Infinite Regresses; 2.1 The regress of causes; 2.2 The regress of reasons; 2.3 The regress of forms; 2.4 The regress of resemblances; 2.5 The regress of temporal series; 2.6 The regress of truths; 2.7 Conclusion
  • 3 Seventeen Paradoxes of the Infinite3.1 A word about paradoxes; 3.2 The arithmetic of infinity; 3.3 The paradox of geometric points; 3.4 Infinite sums; 3.5 Galileo's paradox; 3.6 Hilbert's hotel; 3.7 Gabriel's horn; 3.9 Zeno's paradox; 3.10 The divided stick; 3.11 Thomson's lamp; 3.12 The Littlewood-Ross Banker; 3.13 Benardete's paradox; 3.14 Laraudogoitia's marbles; 3.15 The spaceship; 3.16 The Saint Petersburg paradox; 3.17 The Martingale betting system; 3.18 The delayed heaven paradox; 3.19 Conclusion; Part II Old Theories of Infinity; 4 Impossible Infinite Series: Two False Accounts
  • 4.1 'An infinite series cannot be completed by successive synthesis'4.2 'An infinite series of preconditions cannot be satisfied'; 4.3 Conclusion; 5 Actual and Potential Infinities; 5.1 The theory of potential infinity; 5.2 Why not actual infinities?; 5.3 Infinite divisibility; 5.4 Infinite time; 5.5 Infinite space; 5.6 Infinitely numerous numbers; 5.7 Infinitely numerous abstract objects; 5.8 Infinitely numerous physical objects; 5.9 Conclusion; 6 The Cantorian Orthodoxy; 6.1 The importance of Georg Cantor; 6.2 Sets; 6.3 Cardinal numbers; 6.4 'Greater', 'less', and 'equal'
  • 6.5 Many sets are equally numerous6.6 The diagonalization argument; 6.7 Cantor's theorem; 6.9 Other paradoxes of infinity; 6.10 Conclusion; Part III A New Theory of Infinity and Related Matters; 7 Philosophical Preliminaries; 7.1 Metapreliminaries; 7.2 Phenomenal conservatism; 7.3 Synthetic a priori knowledge; 7.4 Metaphysical possibility; 7.5 Possibility and paradox; 7.6 A realist view of mathematics; 8 Sets; 8.1 Sets are not collections; 8.2 Sets are not defined by the axioms; 8.3 Many regarded as one: the foundational sin?; 8.4 The significance of the paradoxes; 8.5 Are numbers sets?
  • 8.6 Set theory and the laws of arithmetic9 Numbers; 9.1 Cardinal numbers as properties; 9.2 Frege's objection; 9.3 Arithmetical operations; 9.4 The laws of arithmetic; 9.5 Zero; 9.6 A digression on large numbers; 9.7 Magnitudes and real numbers; 9.8 Indexing uses of numbers; 9.9 Other numbers; 10 Infinity; 10.1 Infinity is not a number; 10.2 Infinite cardinalities; 10.3 Infinite extensive magnitudes; 10.4 Infinite intensive magnitudes; 10.5 Some a priori physics; 11 Space; 11.1 Pointy space versus gunky space; 11.2 The unimaginability of points; 11.3 The zero argument
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781137560858
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
ocn950884501
Label
Approaching infinity, Michael Huemer
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover ; Half-Title ; Title ; Copyright ; Dedication ; Contents ; List of Figures; Preface; Part I The Need for a Theory of Infinity; 1 The Prevalence of the Infinite; 1.1 The concept of infinity and the infinite; 1.2 The infinite in mathematics; 1.3 The infinite in philosophy; 1.4 The infinite in the physical world; 1.5 The infinite in modern physics; 1.6 Controversies; 2 Six Infinite Regresses; 2.1 The regress of causes; 2.2 The regress of reasons; 2.3 The regress of forms; 2.4 The regress of resemblances; 2.5 The regress of temporal series; 2.6 The regress of truths; 2.7 Conclusion
  • 3 Seventeen Paradoxes of the Infinite3.1 A word about paradoxes; 3.2 The arithmetic of infinity; 3.3 The paradox of geometric points; 3.4 Infinite sums; 3.5 Galileo's paradox; 3.6 Hilbert's hotel; 3.7 Gabriel's horn; 3.9 Zeno's paradox; 3.10 The divided stick; 3.11 Thomson's lamp; 3.12 The Littlewood-Ross Banker; 3.13 Benardete's paradox; 3.14 Laraudogoitia's marbles; 3.15 The spaceship; 3.16 The Saint Petersburg paradox; 3.17 The Martingale betting system; 3.18 The delayed heaven paradox; 3.19 Conclusion; Part II Old Theories of Infinity; 4 Impossible Infinite Series: Two False Accounts
  • 4.1 'An infinite series cannot be completed by successive synthesis'4.2 'An infinite series of preconditions cannot be satisfied'; 4.3 Conclusion; 5 Actual and Potential Infinities; 5.1 The theory of potential infinity; 5.2 Why not actual infinities?; 5.3 Infinite divisibility; 5.4 Infinite time; 5.5 Infinite space; 5.6 Infinitely numerous numbers; 5.7 Infinitely numerous abstract objects; 5.8 Infinitely numerous physical objects; 5.9 Conclusion; 6 The Cantorian Orthodoxy; 6.1 The importance of Georg Cantor; 6.2 Sets; 6.3 Cardinal numbers; 6.4 'Greater', 'less', and 'equal'
  • 6.5 Many sets are equally numerous6.6 The diagonalization argument; 6.7 Cantor's theorem; 6.9 Other paradoxes of infinity; 6.10 Conclusion; Part III A New Theory of Infinity and Related Matters; 7 Philosophical Preliminaries; 7.1 Metapreliminaries; 7.2 Phenomenal conservatism; 7.3 Synthetic a priori knowledge; 7.4 Metaphysical possibility; 7.5 Possibility and paradox; 7.6 A realist view of mathematics; 8 Sets; 8.1 Sets are not collections; 8.2 Sets are not defined by the axioms; 8.3 Many regarded as one: the foundational sin?; 8.4 The significance of the paradoxes; 8.5 Are numbers sets?
  • 8.6 Set theory and the laws of arithmetic9 Numbers; 9.1 Cardinal numbers as properties; 9.2 Frege's objection; 9.3 Arithmetical operations; 9.4 The laws of arithmetic; 9.5 Zero; 9.6 A digression on large numbers; 9.7 Magnitudes and real numbers; 9.8 Indexing uses of numbers; 9.9 Other numbers; 10 Infinity; 10.1 Infinity is not a number; 10.2 Infinite cardinalities; 10.3 Infinite extensive magnitudes; 10.4 Infinite intensive magnitudes; 10.5 Some a priori physics; 11 Space; 11.1 Pointy space versus gunky space; 11.2 The unimaginability of points; 11.3 The zero argument
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781137560858
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
ocn950884501

Library Locations

Processing Feedback ...