Mathematical Thought: An Introduction to the Philosophy of MathematicsIn contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S. |
Contents
| 1 | |
Proof and Definition by Recursion | 27 |
Systematic Part | 57 |
CHAPTER V | 69 |
THE PARADOXES | 102 |
SIGNIFICS AND LOGIC | 116 |
RECENT DEVELOPMENTS | 124 |
CONCLUDING REMARKS | 174 |
| 193 | |
| 206 | |
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Mathematical Thought: An Introduction to the Philosophy of Mathematics E.W. Beth Limited preview - 1965 |
Common terms and phrases
abstraction analysis appears apply argument Aristotle arithmetic atomic formula axiom system basis Bernays Brouwer Cantor's Chapter characteristica universalis classical mathematics clearly concept concerned conclusion connection considered consistency construction contains deduction defined definition discussion domain dual fractions E. W. Beth elements Euclidean geometry example existence expression fact follows formal logic foundations of mathematics Frege given Gödel Goodstein Hilbert Hoenen inference infinite insight interpretation intuitionism intuitionistic logic intuitionistic mathematics Kant Kant's L. E. J. Brouwer language Leibniz Lorenzen mathe mathematical thinking matics means metalogic metaphysics methods modern logic modus ponens N₁ natural number negation non-Euclidean geometry notion objects paradoxes philosophy of mathematics Plato possible predicate premisses primitive recursive primitive recursive functions principles problem proof question real number respect rôle rules scientific semantic semantic tableau sense sentence sentential logic sequence set-theory significs statement straight line symbolic logic tableau Tarski theorem traditional