Foundations without foundationalism: a case for second-order logic
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Pr.
2002
|
| Edition: | Repr. |
| Series: | Oxford logic guides
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| ISBN: | 0198250290 0198533918 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Foundations without foundationalism
Autor: Shapiro, Stewart
Jahr: 2002
CONTENTS
PART I ORIENTATION
1. Terms and questions l
1.1 Orientation 1
1.2 What is the issue? 10
1.3 Sets and properties 16
2. Foundationalism and foundations of mathematics 25
2.1 Variations and metaphors 26
2.2 Foundations and psychologism 31
2.3 Two conceptions of logic 35
2.4 Marriage: Can there be harmony? 40
2.5 Divorce: Life without completeness 43
2.6 Logic and computation 49
PART II LOGIC AND MATHEMATICS
3. Theory 61
3.1 Language 61
3.2 Deductive systems 65
3.3 Semantics 70
4. Metatheory 79
4.1 First-order theories 79
4.2 Second-order—standard semantics 80
4.3 Non-standard semantics—Henkin and first-order 88
5. Second-order logic and mathematics 96
5.1 Mathematical notions 96
5.2 First-order theories—what goes wrong 110
5.3 Second-order languages and the practice of mathematics 116
5.4 Set theory 127
xx Contents
6. Advanced metatheory 134
6.1 A word on semantic theory 134
6.2 Reductions 137
6.3 Reflection: small large cardinals 141
6.4 Lowenheim-Skolem analogues: large large
cardinals 147
6.5 Characterizations of first-order logic 157
6.6 Definability and other odds and ends 161
PART III HISTORY AND PHILOSOPHY
7. The historical triumph of first-order languages 173
7.1 Introduction 173
7.2 Narrative 177
7.3 To the present 193
8. Second-order logic and rule-following 203
8.1 The regress 204
8.2 Options 208
8.3 Rules and logic 210
9. The competition 220
9.1 Other logics 220
9.2 Free relation variables 246
9.3 First-order set theory 250
References 263
Index 273
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| series2 | Oxford logic guides |
| spelling | Shapiro, Stewart 1951- Verfasser (DE-588)131540564 aut Foundations without foundationalism a case for second-order logic Stewart Shapiro Repr. Oxford Oxford Univ. Pr. 2002 txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 17 Logic, Symbolic and mathematical Sprachlogik (DE-588)4182527-5 gnd rswk-swf Formale Semantik (DE-588)4122144-8 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Formale Semantik (DE-588)4122144-8 s 1\p DE-604 Sprachlogik (DE-588)4182527-5 s 2\p DE-604 Oxford logic guides 17 (DE-604)BV000013997 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010756546&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shapiro, Stewart 1951- Foundations without foundationalism a case for second-order logic Oxford logic guides Logic, Symbolic and mathematical Sprachlogik (DE-588)4182527-5 gnd Formale Semantik (DE-588)4122144-8 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4182527-5 (DE-588)4122144-8 (DE-588)4037951-6 |
| title | Foundations without foundationalism a case for second-order logic |
| title_auth | Foundations without foundationalism a case for second-order logic |
| title_exact_search | Foundations without foundationalism a case for second-order logic |
| title_full | Foundations without foundationalism a case for second-order logic Stewart Shapiro |
| title_fullStr | Foundations without foundationalism a case for second-order logic Stewart Shapiro |
| title_full_unstemmed | Foundations without foundationalism a case for second-order logic Stewart Shapiro |
| title_short | Foundations without foundationalism |
| title_sort | foundations without foundationalism a case for second order logic |
| title_sub | a case for second-order logic |
| topic | Logic, Symbolic and mathematical Sprachlogik (DE-588)4182527-5 gnd Formale Semantik (DE-588)4122144-8 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Sprachlogik Formale Semantik Mathematische Logik |
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