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The Axiomatic Method

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508 pages
mOU 164189tf>DQ^OSMANIA'UNIVERSITY LIBRARYCall ccessionNNo. S'/tf- H(Tltle9This book should returnedbe on or beforethe^latelast marked below.THE AXfOMATJC METHODSTUDIES INLOGICANDTHE FOUNDATIONS OFMATHEMATICSL. E. BROUWERJ.E. W. BETHA. HEYTINGEditors1959NORTH-HOLLAND PUBLISHING COMPANYAMSTERDAMTHE AXIOMATIC METHODWITH SPECIAL REFERENCE TO GEOMETRYAND PHYSICSof an International heldProceedings at theSymposiumof December 1957California, 1958University Berkeley, 26, 4,JanuaryEdited byLEON HENKINMathematicsProfessor of , University of California, BerkeleyPATRICK SUPPESAssociate Profexxor of Philosophy, Stanford UniversityALFRED TARSKTMathematics and JtesearchProfewor of Professor, Universityof California, Berkeleyr1S).>9NOUTH-HOUiAN I) PU I'.LISHING COMPANYAMSTKUDAMNo this book beofpart may reproducedin orany form by microfilm anyprint,other means without written permissionthefrom publisherPRINTED IN THK NETHERLANDSCONTENTSPREFACE VIIPART I. FOUNDATIONS OF GEOMETRYDIE MANNIGFALTIGKEIT DER DIREKTIVEN FUR DIE GKSTALTUNG GEOMETRI-SCHER AXIOMENSYSTEME. Paul ............... 1BernaysWHAT is ELEMENTARY GEOMETRY ? Alfred Tarski ............ 16METAMATHEMATICAL HYPERBOLICSOME PROBLEMS CONCERNING ELEMENTARYGEOMETRY. SzmielewWanda .................... 30DIMENSION IN ELEMENTARY EUCLIDEAN GEOMETRY. Dana Scott ...... 53BINARY RELATIONS AS PRIMITIVE NOTIONS IN ELEMENTARY GEOMETRY.M. Robinson ....................... ...
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mOU 164189 tf> DQ^ OSMANIA'UNIVERSITY LIBRARY Call ccessionNNo. S'/tf- H( Tltle 9 This book should returnedbe on or before the^late last marked below. THE AXfOMATJC METHOD STUDIES INLOGIC AND THE FOUNDATIONS OF MATHEMATICS L. E. BROUWERJ. E. W. BETH A. HEYTING Editors 1959 NORTH-HOLLAND PUBLISHING COMPANY AMSTERDAM THE AXIOMATIC METHOD WITH SPECIAL REFERENCE TO GEOMETRY AND PHYSICS of an International heldProceedings at theSymposium of December 1957California, 1958University Berkeley, 26, 4,January Edited by LEON HENKIN MathematicsProfessor of , University of California, Berkeley PATRICK SUPPES Associate Profexxor of Philosophy, Stanford University ALFRED TARSKT Mathematics and JtesearchProfewor of Professor, University of California, Berkeley r 1S).>9 NOUTH-HOUiAN I) PU I'.LISHING COMPANY AMSTKUDAM No this book beofpart may reproduced in orany form by microfilm anyprint, other means without written permission thefrom publisher PRINTED IN THK NETHERLANDS CONTENTS PREFACE VII PART I. FOUNDATIONS OF GEOMETRY DIE MANNIGFALTIGKEIT DER DIREKTIVEN FUR DIE GKSTALTUNG GEOMETRI- SCHER AXIOMENSYSTEME. Paul ............... 1Bernays WHAT is ELEMENTARY GEOMETRY ? Alfred Tarski ............ 16 METAMATHEMATICAL HYPERBOLICSOME PROBLEMS CONCERNING ELEMENTARY GEOMETRY. SzmielewWanda .................... 30 DIMENSION IN ELEMENTARY EUCLIDEAN GEOMETRY. Dana Scott ...... 53 BINARY RELATIONS AS PRIMITIVE NOTIONS IN ELEMENTARY GEOMETRY. M. Robinson ....................... 68Raphael REMARKS ON PRIMITIVE NOTIONS FOR ELEMENTARY EUCLIDEAN AND NON- KlTCLIDEAN PLANE GEOMETRY. H. L. ............. 86Royden DIRECT INTRODUCTION OF WEIERSTRASS HOMOGENEOUS COORDINATES IN THE HYPERBOLIC ON THE BASIS OF THE ENDCALCULUS OF HlLBERT.PLANE, Paul Szasz ............................ 97 AXIOMATISCHER AUFBAU DER EBENEN ABSOLUTEN GEOMETRIE. 114Bachmann NEW METRIC POSTULATES FOR . . 127ELLIPTIC M-SPACE. Leonard M. Blumenthal AXIOMS FOR GEODESICS AND THEIR IMPLICATIONS. Busemann . . . 146Herbert FOR PLANE AFFINE ..... 160AXIOMS INTUITIONISTIC GEOMETRY. A. Heyting GRUNDLAGEN DER GEOMETRIE VOM STANDPUNKT DER ALLGEMEINEN TOPO- LOGIE AUS. Karol Borsuk ...................... 174 LATTICE-THEORETIC APPROACH TO AND AFFINE GEOMETRY.PROJECTIVE Bjarni ............................. 188J6nsson CONVENTIONALISM IN GEOMETRY. Adolf Griinbaum ........... 204 VI CONTENTS PART II. FOUNDATIONS OF PHYSICS MUCH RIGOR is POSSIBLE IN PHYSICS W.How ? 225Percy Bridgman LA FINITUDE EN SES AXIOMES ET LEURS IMPLICATIONS.MECANIQUE CLASSIQUE, Alexandra Froda 238 THE FOUNDATIONS OF RIGID BODY MECHANICS AND THE DERIVATION OF ITS LAWS FROM THOSE OF PARTICLE MECHANICS. ErilCSt W. Adams 250 THE OF CLASSICAL MECHANICS IN THE LIGHT OF AD-RECENT VANCES IN CONTINUUM MECHANICS. Walter Noll 266 ZUR AXIOMATISIERUNG DER MECHANiK. Hans Hermes 282 AXIOMS FOR RELATIVISTIC KINEMATICS WITH OR WITHOUT PARITY. Patrick 29 1Suppes AXIOMS FOR WalkerCOSMOLOGY. A. G. 308 AXIOMATICMETHOD AND THEORY OF RELATIVITY. OBSERVERSANDEQUIVALENT SPECIAL PRINCIPLE OF RELATIVITY. Yoshio Ueno 322 ON THE FOUNDATIONS OF MECHANICS. Herman Rubin 333QUANTUM INTHE MATHEMATICAL MEANING OF OPERATIONALISM MECHANICS.QUANTUM I.E. 341Segal THEORY FROM POSTULATES. Alfred Lande .... 353QUANTUM NON-QUANTAL UND DAS KOMMUTATiVE GissETZ. Pascual 365QUANTENLOGIK Jordan LOGICAL STRUCTURE OF PHYSICAL THEORIES. Paulette F6vrier 376 PHYSICO-LOGICAL PROBLEMS. L. Dcstouches 390 J. III. GENERAL PROBLEMS AND APPLICATIONSPART OF THE AXIOMATIC METHOD STUDIES IN THE FOUNDATIONS OF GENETICS. H. 408WoodgerJ. IN OF IDENTIFI-AXIOMATIZING A SCIENTIFIC SYSTEM BY AXIOMS THE FORM 429CATIONS. R. B. Braithwaite DEFINABLE AND IN AXIOM SYSTEMS. Herbert A. Simon . . 443TERMS PRIMITIVES AN AXIOMATICTHEORY OF FUNCTIONSAND FLUENTS. Karl 454Menger Wilder . . 474AXIOMATICS AND THE DEVELOPMENT OF CREATIVE TALENT. R. L.
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