Mathematical Thought: An Introduction To The Philosophy Of Mathematics (synthese Library)

In 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. Front Matter....Pages I-XII Introduction....Pages 1-5 Criticism of Mathematics as Based on Naive Intuition....Pages 6-22 The Foundations of Arithmetic....Pages 23-38 Symbolic Logic and Its Connections with Traditional Logic....Pages 39-68 Intuitionism and Formalism....Pages 69-101 The Paradoxes....Pages 102-115 Significs and Logic....Pages 116-123 Recent Developments....Pages 124-173 Concluding Remarks....Pages 174-192 Back Matter....Pages 193-208