Approaching infinity. (2016)

• Record Type: Book
• Further Information: Note: Michael Huemer.
• Authors: Huemer, Michael, 1969-
• 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
• Publisher Details: Basingstoke, Hampshire New York, NY : Palgrave Macmillan
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 111/.6; Philosophy; Infinite; PHILOSOPHY / Metaphysics; Infinite; Mathematics -- History & Philosophy; Philosophy -- Logic; Philosophy of mathematics; Philosophy: logic; Metaphysics; Logic; Philosophy -- Metaphysics; Philosophy: metaphysics & ontology; Electronic books
• Languages: English
• ISBNs: 9781137560872; 1137560878
• Related ISBNs: 9781137560858
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed June 29, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.