From Peirce to Skolem: a neglected chapter in the history of logic
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2000
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Studies in the history and philosophy of mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 468 S. |
| ISBN: | 044450334X |
Internformat
MARC
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| 100 | 1 | |a Brady, Geraldine |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a From Peirce to Skolem |b a neglected chapter in the history of logic |c Geraldine Brady |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2000 | |
| 300 | |a XI, 468 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Studies in the history and philosophy of mathematics |v 4 | |
| 648 | 4 | |a Geschichte 1900-2000 | |
| 648 | 4 | |a Geschichte 1800-1900 | |
| 648 | 7 | |a Geschichte 1870-1923 |2 gnd |9 rswk-swf | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Logic, Symbolic and mathematical |x History |x 19th century | |
| 650 | 4 | |a Logic, Symbolic and mathematical |x History |x 20th century | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804128446416158720 |
|---|---|
| adam_text | Contents
Introduction 1
1. The Early Work of Charles S. Peirce 9
1.1. Overview of the Mathematical Systems of Charles S.
Peirce 9
1.2. Peirce s Influence on the Development of Logic 11
1.3. Peirce s Early Approaches to Logic 14
2. Peirce s Calculus of Relatives: 1870 23
2.1. Peirce s Algebra of Relations 24
2.1.1. Inclusion and Equality 27
2.1.2. Addition 29
2.1.3. Multiplication 30
2.1.4. Peirce s First Quantifiers 38
2.1.5. Involution 39
2.1.6. Involution and Mixed Quantifier Forms 42
2.1.7. Elementary Relatives 44
2.2. Quantification in the Calculus of Relatives in 1870 46
2.3. Summary 48
3. Peirce on the Algebra of Logic: 1880 51
3.1. Overview of Peirce s On the algebra of logic 51
3.2. Discussion 54
3.2.1. The Origins of Logic 54
3.2.2. Syllogism and Illation 56
3.2.3. Forms of Propositions 60
3.2.4. The Algebra of the Copula 64
3.2.5. The Logic of Nonrelative Terms 70
3.3. Conclusion 73
4. Mitchell on a New Algebra of Logic: 1883 75
4.1. Mitchell s Rule of Inference 75
4.2. Single Variable Monadic Logic 78
4.2.1. Single Variable Monadic Propositions 78
4.2.2. Disjunctive Normal Form 80
4.2.3. Rules of Inference for Single Variable Logic 82
4.3. Two Variable Monadic Logic 86
4.3.1. Mitchell s Dimension Theory 86
4.3.2. Contrast to Peirce 88
4.4. Three Variable Monadic Logic 89
4.5. Peirce on Mitchell 90
5. Peirce on the Algebra of Relatives: 1883 95
5.1. Background in Linear Associative Algebras 95
5.2. The Algebra of Relatives 98
5.2.1. Types of Relatives 98
5.2.2. Operations on Relatives 100
5.3. Syllogistic in the Relative Calculus 104
5.4. Prenex Predicate Calculus 106
5.5. Summary of Peirce s Accomplishments in 1883 109
5.5.1. Syntax and Semantics 109
5.5.2. Quantifiers 110
5.6. Peirce s Appraisal of His Algebra of Binary
Relatives 111
6. Peirce s Logic of Quantifiers: 1885 113
6.1. On the Derivation of Logic from Algebra 113
6.2. Nonrelative Logic 116
6.2.1. Embedding Boolean Algebra in Ordinary
Algebra 116
6.2.2. Five Peirce Icons 121
6.2.3. Truth functional Interpretations of Propositions 125
6.3. First Order Logic 127
6.3.1. Infinite Sums and Products 127
6.3.2. Mitchell 128
6.3.3. Formulas and Rules 129
6.4. Second Order Logic 132
7. Schroder s Calculus of Relatives 143
7.1. Die Algebra der Logik: Volume 1 144
7.2. Die Algebra der Logik: Volume 2 147
7.3. Die Algebra der Logik: Volume 3 149
7.3.1. Peirce s Attack on the General Solutions of
Schroder 153
7.3.2. Lectures VI X and Dedekind Chain Theory 155
7.3.3. Lectures XI XII and Higher Order Logic 160
7.4. Norbert Wiener s Ph.D. Thesis 165
8. Lowenheim s Contribution 169
8.1. Overview of Lowenheim s 1915 Paper 171
8.2. Lowenheim s Theorem 172
8.3. Conclusions 191
8.4. Impact of Lowenheim s Paper 195
9. Skolem s Recasting 197
Appendices
1. Schroder s Lecture I 207
2. Schroder s Lecture II 223
3. Schroder s Lecture III 251
4. Schroder s Lecture V 257
5. Schroder s Lecture IX 295
6. Schroder s Lecture XI 339
7. Schroder s Lecture XII 379
8. Norbert Wiener s Thesis 429
Bibliography 445
Index 461
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:22Z |
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| isbn | 044450334X |
| language | English |
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| physical | XI, 468 S. |
| publishDate | 2000 |
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| publisher | Elsevier |
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| series | Studies in the history and philosophy of mathematics |
| series2 | Studies in the history and philosophy of mathematics |
| spelling | Brady, Geraldine Verfasser aut From Peirce to Skolem a neglected chapter in the history of logic Geraldine Brady 1. ed. Amsterdam [u.a.] Elsevier 2000 XI, 468 S. txt rdacontent n rdamedia nc rdacarrier Studies in the history and philosophy of mathematics 4 Geschichte 1900-2000 Geschichte 1800-1900 Geschichte 1870-1923 gnd rswk-swf Geschichte Logic, Symbolic and mathematical History 19th century Logic, Symbolic and mathematical History 20th century Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Geschichte 1870-1923 z DE-604 Studies in the history and philosophy of mathematics 4 (DE-604)BV004415113 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009317084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brady, Geraldine From Peirce to Skolem a neglected chapter in the history of logic Studies in the history and philosophy of mathematics Geschichte Logic, Symbolic and mathematical History 19th century Logic, Symbolic and mathematical History 20th century Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | From Peirce to Skolem a neglected chapter in the history of logic |
| title_auth | From Peirce to Skolem a neglected chapter in the history of logic |
| title_exact_search | From Peirce to Skolem a neglected chapter in the history of logic |
| title_full | From Peirce to Skolem a neglected chapter in the history of logic Geraldine Brady |
| title_fullStr | From Peirce to Skolem a neglected chapter in the history of logic Geraldine Brady |
| title_full_unstemmed | From Peirce to Skolem a neglected chapter in the history of logic Geraldine Brady |
| title_short | From Peirce to Skolem |
| title_sort | from peirce to skolem a neglected chapter in the history of logic |
| title_sub | a neglected chapter in the history of logic |
| topic | Geschichte Logic, Symbolic and mathematical History 19th century Logic, Symbolic and mathematical History 20th century Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Geschichte Logic, Symbolic and mathematical History 19th century Logic, Symbolic and mathematical History 20th century Mathematische Logik |
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