MARC details
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04778cam a22005893i 4500 |
| 001 - CONTROL NUMBER |
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ocn965825348 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20220712044327.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION |
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m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr cnu|||unuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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161213s2016 xx o 000 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
N$T |
| Language of cataloging |
eng |
| Description conventions |
rda |
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pn |
| Transcribing agency |
N$T |
| Modifying agency |
EBLCP |
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N$T |
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OCLCO |
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OCLCF |
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ESU |
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OCLCQ |
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OCLCO |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780191063800 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
0191063800 |
| Qualifying information |
(electronic bk.) |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)965825348 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA9 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
039000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
023000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
026000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510.1 |
| Edition number |
23 |
| 049 ## - LOCAL HOLDINGS (OCLC) |
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| Holding library |
MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Mancosu, Paolo. |
| 9 (RLIN) |
165955 |
| 245 10 - TITLE STATEMENT |
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| Title |
Abstraction and Infinity. |
| 264 #1 - |
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[Place of publication not identified] : |
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OUP Premium : |
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OUP Oxford, |
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2016. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource |
| 336 ## - |
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text |
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txt |
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rdacontent |
| 337 ## - |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 588 0# - |
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Vendor-supplied metadata. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Cover; Abstraction and Infinity; Copyright; Dedication; Contents; Introduction; Abstraction; Infinity; Abstraction and Infinity; Acknowledgements; 1: The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond); 1.1 Introduction; 1.2 Equivalence relations, invariants, and definitions by abstraction; 1.3 Mathematical practice and definitions by abstraction in classical geometry; 1.4 Definitions by abstraction in number theory, number systems, geometry, and set theory during the XIXth century; 1.4.1 Number theory; 1.4.2 Systems of Numbers and abstraction principles |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1.4.3 Complex numbers and geometrical calculus1.4.4 SetTheory; 1.5 Conclusion; 2: The logical and philosophical reflection on definitions by abstraction: From Frege to the Peano school and Russell; 2.1 Frege's Grundlagen, section ; 2.1.1 The Grassmannian influence on Frege: Abstraction principles in geometry; 2.1.2 The proper conceptual order and Frege's criticism of the definition of parallels in terms of directions; 2.1.3 Aprioricity claims for the concept of direction: Schlömilch's Geometrie des Maasses; 2.1.4 The debate over Schlömilch's theory of directions |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
2.2 The logical discussion on definitions by abstraction2.2.1 Peano and his school; 2.2.2 Russell and Couturat; 2.2.3 Padoa on definitions by abstraction and further developments; 2.3 Conclusion; 2.4 Appendix; 3: Measuring the size of infinite collections of natural numbers: Was Cantor's theory of infinite number inevitable?; 3.1 Introduction; 3.2 Paradoxes of the infinite up to the middle ages; 3.3 Galileo and Leibniz; 3.4 Emmanuel Maignan; 3.5 Bolzano and Cantor; 3.6 Contemporary mathematical approaches tomeasuring the size of countably infinite sets |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
3.6.1 Katz's "Sets and their Sizes" (1981)3.6.2 A theory of numerosities; 3.7 Philosophical remarks; 3.7.1 An historiographical lesson; 3.7.2 Gödel's claim that Cantor's theory of size for infinite sets is inevitable; 3.7.3 Generalization, explanation, fruitfulness; 3.8 Conclusion; 4: In good company? On Hume's Principle and the assignment of numbers to infinite concepts; 4.1 Introduction; 4.2 Neo-logicism and Hume's Principle; 4.3 Numerosity functions: Schröder, Peano, and Bolzano; 4.4 A plethora of good abstractions; 4.5 Neo-logicism and Finite Hume's Principle |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
4.6 The 'good company' objection as a generalization of Heck's argument4.7 HP's good companions and the problem of cross-sortal identity; 4.8 Conclusion; 4.9 Appendix 1; 4.10 Appendix 2 ; Bibliography; Name Index |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems. |
| 590 ## - LOCAL NOTE (RLIN) |
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| Local note |
eBooks on EBSCOhost |
| Provenance (VM) [OBSOLETE] |
EBSCO eBook Subscription Academic Collection - Worldwide |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| General subdivision |
Philosophy. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Infinite. |
| 9 (RLIN) |
63710 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathématiques |
| General subdivision |
Philosophie. |
| 9 (RLIN) |
884092 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Infini. |
| 9 (RLIN) |
990035 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
infinity. |
| Source of heading or term |
aat |
| 9 (RLIN) |
990036 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Essays. |
| Source of heading or term |
bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Pre-Calculus. |
| Source of heading or term |
bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Reference. |
| Source of heading or term |
bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Infinite. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst00972421 |
| 9 (RLIN) |
63710 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| General subdivision |
Philosophy. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst01012213 |
| 655 #4 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1435311">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1435311</a> |
| 938 ## - |
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ProQuest Ebook Central |
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EBLB |
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EBL4766846 |
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EBSCOhost |
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EBSC |
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1435311 |
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92 |
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INOPJ |
