An invitation to formal reasoning: the logic of terms
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Aldershot [u.a.]
Ashgate
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 260 S. graph. Darst. |
| ISBN: | 0754613666 |
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Record in the Search Index
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|---|---|
| adam_text | Titel: An invitation to formal reasoning
Autor: Sommers, Fred
Jahr: 2000
Contents
Preface x
Chapter 1 Reasoning
1. Introduction 1
2. The Form of an Argument 4
3. A Word About the Form of Statements 4
4. The Form of Singular Statements 5
5. Terms and Statements 7
6. Symbolizing Compound Statements 9
7. A Word About Validity 11
8. How Material Expressions are Meaningful 13
9. Terms 13
10. Some Terms are Vacuous 14
11. Statement Meaning 17
12. Truth and Correspondence to Facts 19
13. Propositions 20
14. States of Affairs 21
15. The facts and the FACTS 22
16. What Statements Denote 22
17. Summary and Discussion on the Meaning of Statements 23
Chapter 2 Picturing Propositions
1. State Diagrams 25
2. Representing Singular Propositions 28
3. Entailments 30
4. Negative Entailments 33
5. STATES and states 35
6. Positive and Negative Valence 36
7. The Limitations of State Diagrams 36
8. The Statement Use of Sentences 38
9. Truth Relations 39
10. Logical Syntax 40
vi An Invitation to Formal Reasoning
11. Term Way vs. Predicate Way 43
12. Some Useful Terminology 45
13. Subjects and Predicates 46
Chapter 3 The Language of Logic (I)
1. Introduction 49
2. Writing Y some X as an Algebraic Expression 50
3. Affirmation (+) and Denial (-) 50
4. Binary and Unary Uses of a Sign 51
5. Positive and Negative Valence 51
6. Contrary Terms and Sentences 52
7. Every 53
8. Why Some Equal Sentences are not Logically Equivalent 54
9. E-forms and A-forms 55
10. Transcribing Affirmative Statements 56
11. How to Tell the Valence of E-form Statements 57
12. Negative Valence = Universal Quantity 57
13. The Law of Commutation in E-form 5 8
14. Every in E-form Transcriptions 59
15. Isn t 61
16. The General Conditions of Equivalence 61
17. The General Form of Statements 64
18. The Logical Law of Commutation Applied to Compound
Terms 67
19. The Logical Law of Association 68
20. Derivations 69
21. More on Regimenting Sentences 71
22. Uniquely Denoting Terms and Singular Statements 73
23. Identities 76
Chapter 4 The Language of Logic (IT)
1. Compound Statements 77
2. If.then 78
3. More on Transcription 80
4. Or 81
5. Representing Internal Structures 83
6. The General Form of Compound Statements 85
7. Direct Transcriptions 86
Contents vii
8. Relational Statements 88
9. A Word About Pairing 89
10. Subject/Predicate; Predicate/Subject 91
11. Dyadic Normal Forms 92
12. Commuting Relational Terms 93
13. Immediate Inferences from Relational Statements 95
14. Obversion 96
15. The Passive Transformation 97
16. Simplification 98
17. Pronouns and Proterms 99
Appendix to Chapter 4
18. Bounded Denotation 102
19. Terms in their Contexts 103
20. Rules for Using Markers 106
Chapter 5 Syllogistic
1. Validity 109
2. Inference 114
3. Enthymemes 118
4. Why REGAL Works 122
5. Inconsistent Conjunctions: The Tell-tale Characteristics 124
6. Equivalent Conjunctions 127
7. How This is Related to REGAL 128
8. Syllogisms with Singular Statements 129
9. The Laws of Identity 130
10. Proofs of These Laws 131
11. The Matrix Method for Drawing Conclusions 133
12. Venn Diagrams 135
Chapter 6 Relational Syllogisms
1. Introduction 139
2. Applying the Dictum to Relational Arguments 140
3. Distributed Terms 141
4. Applying DDO 143
5. Indirect Proofs for Relational Arguments 147
6. Transforming Arguments 148
7. Annotating a Proof of Validity 150
8. Arguing with Pronominal Sentences 151
viii An Invitation to Formal Reasoning
9. Distributed Proterms 158
Chapter 7 Statement Logic
1. Introduction 163
2. Contradictions 165
3. Tautology 166
4. Inconsistent Statements 167
5. Contingent Statements 167
6. Direct Proofs 168
7. Rules of Statement Logic Used in Proofs 169
8. Disjunctive Normal Forms (DNF) 175
9. Inconsistency and Validity 176
10. Graphic Representation of Compound Statements 178
11. Regimenting Statements for Treeing 183
12. Large Trees 185
13. Drawing Conclusions 192
14. Partial Disjunctions 193
15. Using the Tree Method for Annotated Proofs 199
16. Statement Logic as a Special Branch of Syllogistic Logic 201
17. Venn Diagrams for the Singleton Universe of Propositional
Logic 209
Chapter 8 Modern Predicate Logic
1. Syntax 213
2. MPL: The Predicate Way 214
3. General Sentences in MPL 215
4. The Logical Language of MPL 216
5. Singular Sentences in MPL 220
6. How the Logical Syntax of MPL is Ontologically Explicit 222
7. Dyadic Normal Forms 224
8. Translating Pronominalizations 227
9. Preparing the TFL Bridge 229
10. Identity in MPL 230
11. Logical Reckoning in MPL 232
12. Transformation Rules 233
13. Rules of Inference 235
14. Literal Formulas 237
15. Reckoning in MPL 240
Contents ix
16. Canonical Normal Forms (CNF) 241
17. Indirect Proofs in MPL 242
18. Relational MPL Arguments 244
19. Identity Arguments in MPL 249
Rules, Laws and Principles 253
A Note on Further Reading 259
|
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| spelling | Sommers, Fred Verfasser aut An invitation to formal reasoning the logic of terms Fred Sommers ; George Englebretsen Aldershot [u.a.] Ashgate 2000 XVI, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Logik (DE-588)4036202-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Logik (DE-588)4036202-4 s DE-604 Englebretsen, George Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008998163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sommers, Fred Englebretsen, George An invitation to formal reasoning the logic of terms Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4151278-9 |
| title | An invitation to formal reasoning the logic of terms |
| title_auth | An invitation to formal reasoning the logic of terms |
| title_exact_search | An invitation to formal reasoning the logic of terms |
| title_full | An invitation to formal reasoning the logic of terms Fred Sommers ; George Englebretsen |
| title_fullStr | An invitation to formal reasoning the logic of terms Fred Sommers ; George Englebretsen |
| title_full_unstemmed | An invitation to formal reasoning the logic of terms Fred Sommers ; George Englebretsen |
| title_short | An invitation to formal reasoning |
| title_sort | an invitation to formal reasoning the logic of terms |
| title_sub | the logic of terms |
| topic | Logik (DE-588)4036202-4 gnd |
| topic_facet | Logik Einführung |
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