The logic of number:
In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstracti...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2022
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable 'single-barreled' abstraction, in contrast with the 'double-barreled' abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle. |
| Beschreibung: | xii, 363 Seiten 24 cm |
| ISBN: | 9780192846679 |
Internformat
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| 505 | 8 | |a Part I: Natural Logicism -- Part II: Natural Logicism and the Naturals -- Part III: Natural Logicism and the Rationals -- Part IV: Natural Logicism and the Reals | |
| 520 | 3 | |a In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable 'single-barreled' abstraction, in contrast with the 'double-barreled' abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle. | |
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Datensatz im Suchindex
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| adam_text | Contents xi Acknowledgments I Naturai Logicism 1 1 What is Natural Logicism? 3 2 Before and After Frege 17 3 After Gentzen 21 4 Foundations After Gödel 35 5 Logico-Genetic Theorizing 49 Natural Logicism and the Naturals 65 6 Introduction, with Some Historical Background 67 7 Denoting Numbers 75 8 Exact Numerosity 81 II 9 The Adequacy Condition Involving Schema N 93 10 The Rules of Constructive Logicism 101 11 Formal Results of Constructive Logicism 109 12 Reflections on Counting 129 13 Formal Results about the Inductively Defined Numerically Exact Quantifiers 137 ix
Contents III Natural Logicism and the Rationals 153 14 What Would a Gifted Child Need in Order to Grasp Fractions? The Case of Edwin 155 15 Past Accounts of the Rationals as Ratios 163 16 Mereology and Fraction Abstraction 177 17 Taking Stock and Glimpsing Beyond 195 IV Natural Logicism and the Reals 199 18 The Trend toward Arithmetization 201 19 Resisting the Trend toward Arithmetization 217 20 Impurities and Incompletenesses 233 21 The Concept of Real Number 241 22 Geometric Concepts and Axioms 261 23 Bicimals 295 24 Uncountability 301 25 Back to Bicimals 319 Appendix A Proof of the Non-Compossibility Theorem 333 Appendix В Formal Proof of a Geometric Inference 339 Bibliography 341 Index 355
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| adam_txt |
Contents xi Acknowledgments I Naturai Logicism 1 1 What is Natural Logicism? 3 2 Before and After Frege 17 3 After Gentzen 21 4 Foundations After Gödel 35 5 Logico-Genetic Theorizing 49 Natural Logicism and the Naturals 65 6 Introduction, with Some Historical Background 67 7 Denoting Numbers 75 8 Exact Numerosity 81 II 9 The Adequacy Condition Involving Schema N 93 10 The Rules of Constructive Logicism 101 11 Formal Results of Constructive Logicism 109 12 Reflections on Counting 129 13 Formal Results about the Inductively Defined Numerically Exact Quantifiers 137 ix
Contents III Natural Logicism and the Rationals 153 14 What Would a Gifted Child Need in Order to Grasp Fractions? The Case of Edwin 155 15 Past Accounts of the Rationals as Ratios 163 16 Mereology and Fraction Abstraction 177 17 Taking Stock and Glimpsing Beyond 195 IV Natural Logicism and the Reals 199 18 The Trend toward Arithmetization 201 19 Resisting the Trend toward Arithmetization 217 20 Impurities and Incompletenesses 233 21 The Concept of Real Number 241 22 Geometric Concepts and Axioms 261 23 Bicimals 295 24 Uncountability 301 25 Back to Bicimals 319 Appendix A Proof of the Non-Compossibility Theorem 333 Appendix В Formal Proof of a Geometric Inference 339 Bibliography 341 Index 355 |
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| contents | Part I: Natural Logicism -- Part II: Natural Logicism and the Naturals -- Part III: Natural Logicism and the Rationals -- Part IV: Natural Logicism and the Reals |
| ctrlnum | (OCoLC)1319726033 (DE-599)BVBBV048556977 |
| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:58:53Z |
| indexdate | 2024-07-10T09:41:24Z |
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| isbn | 9780192846679 |
| language | English |
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| physical | xii, 363 Seiten 24 cm |
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| spelling | Tennant, Neil 1950- Verfasser (DE-588)138937672 aut The logic of number Neil Tennant Oxford Oxford University Press 2022 xii, 363 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier Part I: Natural Logicism -- Part II: Natural Logicism and the Naturals -- Part III: Natural Logicism and the Rationals -- Part IV: Natural Logicism and the Reals In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable 'single-barreled' abstraction, in contrast with the 'double-barreled' abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle. Natürliche Zahl (DE-588)4041357-3 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Arithmetic / Foundations Logic Arithmétique / Fondements Natürliche Zahl (DE-588)4041357-3 s Logik (DE-588)4036202-4 s DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033933242&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tennant, Neil 1950- The logic of number Part I: Natural Logicism -- Part II: Natural Logicism and the Naturals -- Part III: Natural Logicism and the Rationals -- Part IV: Natural Logicism and the Reals Natürliche Zahl (DE-588)4041357-3 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4041357-3 (DE-588)4036202-4 |
| title | The logic of number |
| title_auth | The logic of number |
| title_exact_search | The logic of number |
| title_exact_search_txtP | The logic of number |
| title_full | The logic of number Neil Tennant |
| title_fullStr | The logic of number Neil Tennant |
| title_full_unstemmed | The logic of number Neil Tennant |
| title_short | The logic of number |
| title_sort | the logic of number |
| topic | Natürliche Zahl (DE-588)4041357-3 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Natürliche Zahl Logik |
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