Provability, Computability and Reflection (eBook)

Lev D. Beklemishev (Autor)

eBook Download: PDF

2000 | 1. Auflage
360 Seiten
Elsevier Science (Verlag)
978-0-08-095750-0 (ISBN)

Infos

Provability, Computability and Reflection

Inhalt

Front Cover 1
The Logical Systems of Lesniewski 4
Copyright Page 5
Contents 6
CHAPTER 1. CONVENTIONS OF EXPOSITION AND REFERENCE 10
1.0 Reference to sources 10
1.1 Italics and quotation 10
1.2 Quotation names 11
1.3 Reference to individual expressions 13
1.4 Definitions 14
1.5 Nouns and names 15
1.6 Verbs 16
1.7 Technical use of English expressions 17
1.8 Material mode of expression 23
CHAPTER 2. LESNIEWSKI’S DEVELOPMENT 27
2.0 Background and associates 27
2.1 Early work and publications 29
2.2 Research in Warsaw 33
2.3 Mature publications 34
CHAPTER 3. LESNIEWSKI’S ACHIEVEMENTS 36
3.1 Refutation of a “platonist” theory of “representation” 36
3.2 Formalization of logic and foundations of mathematics 37
3.3 Resolution of paradoxes 38
3.4 Contributions to semantics 42
3.5 Principles of formalization 45
3.6 Axiomatic reductions 48
3.7 Natural deduction by the suppositional method 49
3.8 Ideographic notation for propositional logic 50
3.9 Other peripheral contributions 51
3.10 Why is Lesniewski’s work relatively unknown? 52
CHAPTER 4. LESNIEWSKI’S CRITIQUE OF PURE FORMALISM 58
4.1 “Thorough pragmatism” 62
4.2 “Useful nonsense” 63
4.3 Convenient carelessness 65
4.4 “Names” which name nothing 65
4.5 “Identification” of discernibles 66
4.6 Convenient fictions and possible interpretations 67
4.7 Formal simplification and philosophical clarification 70
4.8 Treatment of antinomies 73
4.9 Initial analysis of Russell’s contradiction 75
4.10 “Collections not actually composed of their elements” 78
4.11 Lesniewski's assessment of other systems 87
4.12 Avoidance of misconceptions 88
CHAPTER 5. LESNIEWSKI‘S GRAMMAR OF SEMANTIC CATEGORIES 93
5.1 Rationale of logical grammar 94
5.2 Construction of Lesniewski’s grammar 101
5.3 Propositions 107
5.4 Do Lesniewski’s requirements preclude vicious circles? 109
CHAPTER 6. LESNIEWSKI’S SYSTEM OF LOGIC AND FOUNDATIONS OF MATHEMATICS 114
6.0 Conception of logic 114
6.1 Formalization 115
6.2 Lesniewski’s system of logic 149
6.3 Mereology 158
6.4 Demonstrable relative consistency 162
6.5 Grzegorczyk on Lesniewski 163
CHAPTER 7. TERMINOLOGICAL EXPLANATIONS AND DIRECTIVES 176
7.0 Preliminary explanations 176
7.1 Terminological explanations 186
7.2 The first five directives for this system of logic 274
7.3 Terminological explanations peculiar to ontology 275
7.4 Final directives for this system of logic 297
CHAPTER 8. PRINCIPLES OF LESNIEWSKI’S IDEOGRAPHIC NOTATION 298
9. NOTES 315
10. BIBLIOGRAPHY 329
10.0 Primary sources 329
10.1 Other publications cited 333
11. INDEX 343
11.1 Unalphabetized technical symbols 343
11.2 Authors and subjects 344

Produkt-Details

• Erscheint lt. Verlag: 1.4.2000
• Sprache: englisch
• Themenwelt: Informatik ► Software Entwicklung ► User Interfaces (HCI)
• Themenwelt: Informatik ► Theorie / Studium ► Algorithmen
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-095750-1 / 0080957501
• ISBN-13: 978-0-08-095750-0 / 9780080957500