Symbolic logic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Macmillan
1979
London Collier Macmillan |
| Ausgabe: | 5. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 398 S. |
| ISBN: | 0023249803 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
I Introduction: Logic and Language 1
1.1 What Is Logic? 1
1.2 The Nature of Argument 2
1.3 Truth and Validity 4
1.4 Symbolic Logic 5
CZ Arguments Containing Compound Statements 8
2.1 Simple and Compound Statements 8
2.2 Conditional Statements 16
2.3 Argument Forms and Truth Tables 19
2.4 Statement Forms 27
3 The Method of Deduction 32
3.1 Formal Proof of Validity 32
3.2 The Rule of Replacement 39
3.3 Proving Invalidity 48
3.4 The Rule of Conditional Proof 49
3.5 The Rule of Indirect Proof 52
3.6 Proofs of Tautologies 54
3.7 The Strengthened Rule of Conditional Proof 56
3.8 Shorter Truth Table Technique—Reductio ad
Absurdum Method 61
4 Quantification Theory 63
4.1 Singular Propositions and General
Propositions 63
4.2 Proving Validity: Preliminary Quantification
Rules 71
4.3 Proving Invalidity 78
4.4 Multiply General Propositions 83
xi
xii Contents
4.5 Quantification Rules 89
4.6 More on Proving Invalidity 105
4.7 Logical Truths Involving Quantifiers 108
5 The Logic of Relations 116
5.1 Symbolizing Relations 116
5.2 Arguments Involving Relations 130
5.3 Some Attributes of Relations 134
5.4 Identity and the Definite Description 140
5.5 Predicate Variables and Attributes of
Attributes 150
6 Deductive Systems 157
6.1 Definition and Deduction 157
6.2 Euclidean Geometry 158
6.3 Formal Deductive Systems 162
6.4 Attributes of Formal Deductive Systems 164
6.5 Logistic Systems 166
7 Set Theory 170
7.1 The Algebra of Classes 170
7.2 Axioms for Class Algebra 175
7.3 Zermelo Fraenkel Set Theory (ZF)—The First Six
Axioms 176
7.4 Relations and Functions 185
7.5 Natural Numbers and the Axiom of Infinity 190
7.6 Cardinal Numbers and the Choice Axiom 195
7.7 Ordinal Numbers and the Axioms of Replacement
and Regularity 202
8 A Propositional Calculus 213
8.1 Object Language and Metalanguage 213
8.2 Primitive Symbols and Well Formed
Formulas 215
8.3 Axioms and Demonstrations 227
8.4 Independence of the Axioms 231
8.5 Development of the Calculus 237
8.6 Deductive Completeness 250
Contents xiii
S Alternative Systems and Notations 259
9.1 Alternative Systems of Logic 259
9.2 The Hilbert Ackermann System 260
9.3 The Use of Dots as Brackets 276
9.4 A Parenthesis Free Notation 279
9.5 The Stroke and Dagger Operators 281
9.6 The Nicod System 282
A First Order Function Calculus 290
1O 10.1 The New Logistic System RSX 290
10.2 The Development of 1^ 296
10.3 Duality 302
10.4 RSj and the 'Natural Deduction'
Techniques 307
10.5 Normal Forms 311
10.6 Completeness of RSj 318
10.7 RSi with Identity 328
10.8 First Order Logic Including ZF Set Theory 331
Appendix A: Incompleteness of the Nineteen Rules 333
Appendix B: Normal Forms and Boolean Expansions 337
Appendix C: The Ramified Theory of Types 344
Solutions to Selected Exercises 355
Special Symbols 381
Index 385 |
| any_adam_object | 1 |
| author | Copi, Irving M. 1917-2002 |
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| dewey-full | 511/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.3 |
| dewey-search | 511/.3 |
| dewey-sort | 3511 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 5. ed. |
| format | Book |
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| id | DE-604.BV001950646 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-01T16:00:41Z |
| institution | BVB |
| isbn | 0023249803 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001271626 |
| oclc_num | 4076502 |
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| physical | XIII, 398 S. |
| psigel | TUB-nveb |
| publishDate | 1979 |
| publishDateSearch | 1979 |
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| publisher | Macmillan Collier Macmillan |
| record_format | marc |
| spelling | Copi, Irving M. 1917-2002 Verfasser (DE-588)12049275X aut Symbolic logic Irving M. Copi 5. ed. New York Macmillan 1979 London Collier Macmillan XIII, 398 S. txt rdacontent n rdamedia nc rdacarrier Logique symbolique et mathématique Logic, Symbolic and mathematical Lyrik (DE-588)4036774-5 gnd rswk-swf Symbol (DE-588)4058716-2 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Lyrik (DE-588)4036774-5 s Symbol (DE-588)4058716-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001271626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Copi, Irving M. 1917-2002 Symbolic logic Logique symbolique et mathématique Logic, Symbolic and mathematical Lyrik (DE-588)4036774-5 gnd Symbol (DE-588)4058716-2 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4036774-5 (DE-588)4058716-2 (DE-588)4037951-6 |
| title | Symbolic logic |
| title_auth | Symbolic logic |
| title_exact_search | Symbolic logic |
| title_full | Symbolic logic Irving M. Copi |
| title_fullStr | Symbolic logic Irving M. Copi |
| title_full_unstemmed | Symbolic logic Irving M. Copi |
| title_short | Symbolic logic |
| title_sort | symbolic logic |
| topic | Logique symbolique et mathématique Logic, Symbolic and mathematical Lyrik (DE-588)4036774-5 gnd Symbol (DE-588)4058716-2 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logique symbolique et mathématique Logic, Symbolic and mathematical Lyrik Symbol Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001271626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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