Foundations without foundationalism : a case for second-order logic
著者
書誌事項
Foundations without foundationalism : a case for second-order logic
（Oxford logic guides, 17）
Clarendon Press , Oxford University Press, 1991
- : pbk
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注記
Bibliography: p. [263]-272
Includes index
内容説明・目次
内容説明
Stewart Shapiro presents a distinctive and persuasive view of the foundations of mathematics, arguing controversially that second-order logic has a central role to play in laying these foundations. To support this contention, he first gives a detailed development of second-order and higher-order logic, in a way that will be accessible to graduate students. He then demonstrates that second-order notions are prevalent in mathematics as practised, and that higher-order
logic is needed to codify many contemporary mathematical concepts. Throughout, he emphasizes philosophical and historical issues that the subject raises. Foundations without Foundationalism is a key contribution both to philosophy of mathematics and to mathematical logic.
'In this excellent treatise Shapiro defends the use of second-order languages and logic as framework for mathematics. His coverage of the wide range of logical and philosophical topics required for understanding the controversy over second-order logic is thorough, clear, and persuasive. . . . Shapiro recognizes that it is unlikely that he has had the last word on these controversial philosophical subjects. Nevertheless, his book is certainly an excellent place to start work on them.' Michael
D. Resnik, History and Philosophy of Logic
目次
- PART I: ORIENTATION
- 1. TERMS AND QUESTIONS
- 2. FOUNDATIONALISM AND FOUNDATIONS OF MATHEMATICS
- PART II: LOGIC AND MATHEMATICS
- 3. THEORY
- 4. METATHEORY
- 5. SECOND-ORDER LOGIC AND MATHEMATICS
- 6. ADVANCED METATHEORY
- PART III: HISTORY AND PHILOSOPHY
- 7. THE HISTORICAL 'TRIUMPH' OF FIRST-ORDER LANGUAGES
- 8. SECOND-ORDER LOGIC AND RULE-FOLLOWING
- 9. THE COMPETITION
- REFERENCES
- INDEX
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