On Constructive Interpretation of Predictive Mathematics (1990)

Informationen zum Autor Charles Parsons Zusammenfassung First published in 1990, this book consists of a detailed exposition of results of the theory of "interpretation" developed by G. Kreisel — the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work. Inhaltsverzeichnis Preface; Chapter I. Introduction; 1. Statement of the Problem 2. Systems Considered 3. Metamathematical Methods of Proof; Chapter II. Over-Simple Interpretations; 1. Trivial Interpretation 2. Failure of Interpretation by Recursive Satisfaction 3. Dependence of the Proof of the Verifiable Formula corresponding to a Theorem; Chapter III. Herbrand Interpretation; 1. The Concept of Herbrand Interpretation 2. Herbrand Interpretation of Elementary Number Theory without Induction 3. Properties of the Interpretation 4. Impossibility of an Herbrand Interpretation of Number Theory with Induction; Chapter IV. The No-Counter-Example Interpretation of Number Theory; 1. Non-constructive Considerations 2. No-Counter-Example Interpretation of Number Theory without Induction 3. No-Counter-Example Interpretation, 1*-Consistency, and External Consistency 4. Ordinal Recursive Functionals, 1*-Consistency of Number Theory with Induction 5. Representation of Ordinal Recursive Functionals in Elementary Number Theory; Chapter V. Ramified Analysis; 1. Description of Systems 2. Ramified Analysis without Induction 3. Recursive Well-orderings and Ordinal Recursive Functionals 4. Ramified Analysis with Induction 5. Representation of Ordinal Recursive Functionals in Ramified Analysis; Chapter VI. O-Consistency; 1. Critique of the Concept of ?-Consistency 2. O-Consistency, External Consistency, and 1*-Consistency 3. O-Consistency of Ramified Analysis; Appendix I. Arithmetization of Schütte’s Cut-elimination theorems; Appendix II. Ordinal Functions; Bibliography; Index of Definitions ...

Product details

• Authors: Charles Parsons
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 08.08.2016
• EAN: 9781138226524
• ISBN: 978-1-138-22652-4
• No. of pages: 342
• Series: Routledge Revivals; Routledge Revivals
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > General, dictionaries; PHILOSOPHY / General, PHILOSOPHY / Logic, Philosophy, PHILOSOPHY / Movements / Analytic, PHILOSOPHY / Methodology, PHILOSOPHY / Movements / Critical Theory, PHILOSOPHY / Movements / Empiricism, Philosophy of Mathematics, Western philosophy from c 1800, Probability & statistics, Mathematical logic, Philosophy: logic, Probability and statistics, Western philosophy: Enlightenment, Analytical philosophy and Logical Positivism