The Resource Approaching infinity, Michael Huemer
Approaching infinity, Michael Huemer
Resource Information
The item Approaching infinity, Michael Huemer represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Approaching infinity, Michael Huemer represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource.
- 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
- Isbn
- 9781137560858
- Label
- Approaching infinity
- Title
- Approaching infinity
- Statement of responsibility
- Michael Huemer
- 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
- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Approaching-infinity-Michael-Huemer/84nSTbfuY8o/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Approaching-infinity-Michael-Huemer/84nSTbfuY8o/">Approaching infinity, Michael Huemer</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">Sydney Jones Library, University of Liverpool</a></span></span></span></span></div>
