Philosophical introduction to set theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Notre Dame u.a.
Univ. of Notre Dame Pr.
1990
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 180 S. |
| ISBN: | 0268015848 0268015856 |
Internformat
MARC
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| 245 | 1 | 0 | |a Philosophical introduction to set theory |c Stephen Pollard |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface xi
I. Queen of the Formal Sciences 1
1. Mathematical Glue, 1
2. Mathematics One Foundation, 4
3. Science of the Infinite, 6
4. But What Are Sets?, 12
II. Offspring of Analysis 13
1. A Role for History, 13
2. Greek Roots, 15
3. The Latitude of Forms, 17
4. Eidetic Logistic, 20
5. Genitum and Functio, 23
6. Functions as Notation, 25
7. Cantor the Analyst, 27
8. Numbers, Functions, Sets, 32
9. Dedekind Cuts, 33
10. Frege on Abstraction, 36
III. COMMONSENSE SETS 40
1. Nausea, 40
2. The Court of Ordinary Language, 41
3. Black on Sets as Commonsense Objects, 42
4. Sets and Plural Reference, 44
5. Zermelian Sets, 51
vii
i
viii Contents
IV. Logical Interlude: Intebpretability 56
1. The Age of Logic?, 56
2. Interpretation Functions, 57
3. Abstraction as Interpretation, 59
4. Pseudo Uniqueness, 63
V. Formalism 65
1. Universal Theories as Mathematical
Objects, 65
2. Cantor s Continuum Hypothesis, 67
3. The Robinson Cohen Challenge, 70
4. A Dummettian Argument, 72
5. Why Bother?, 79
VI. Some Metamathematics 82
1. A Formal Language and Its Logic, 82
2. The Principle of Comprehension, 85
3. Interpretation of the Successor Function, 89
VII. Logical Interlude: Second Order Logic 97
1. Logics of the First and Higher Orders, 97
2. A Monadic Second Order Deductive
System, 100
3. Boolos on Monadic Second Order Logic, 103
4. Second Order Z, 106
5. CH Is Second Order Decidable, 110
VIII. Iterative Hierarchies 115
1. Set Formation, 115
2. Weil Ordered Structures, 117
3. Choosing a Theory, 119
4. Theory Tlf 121
5. Theory T2, 129
6. A Modification of T2, 133
7. Universal Structures, 135
Contents ix
IX. Structuralism 138
1. Stenius on Sets and Structures, 138
2. Reference and Reduction, 143
3. Resnik s Mathematical Structuralism, 148
Appendix I 155
Appendix II 161
Notes 165
Bibliography 173
Index of Names 179
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T16:09:27Z |
| institution | BVB |
| isbn | 0268015848 0268015856 |
| language | English |
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| physical | XII, 180 S. |
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| spelling | Pollard, Stephen Verfasser aut Philosophical introduction to set theory Stephen Pollard Notre Dame u.a. Univ. of Notre Dame Pr. 1990 XII, 180 S. txt rdacontent n rdamedia nc rdacarrier Set theory Philosophie (DE-588)4045791-6 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 Philosophie (DE-588)4045791-6 s DE-188 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002603044&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pollard, Stephen Philosophical introduction to set theory Set theory Philosophie (DE-588)4045791-6 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4074715-3 |
| title | Philosophical introduction to set theory |
| title_auth | Philosophical introduction to set theory |
| title_exact_search | Philosophical introduction to set theory |
| title_full | Philosophical introduction to set theory Stephen Pollard |
| title_fullStr | Philosophical introduction to set theory Stephen Pollard |
| title_full_unstemmed | Philosophical introduction to set theory Stephen Pollard |
| title_short | Philosophical introduction to set theory |
| title_sort | philosophical introduction to set theory |
| topic | Set theory Philosophie (DE-588)4045791-6 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Set theory Philosophie Mengenlehre |
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