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 ....................... ...
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 METHODSTUDIES INLOGIC
AND
THE FOUNDATIONS OF
MATHEMATICS
L. E. BROUWERJ.
E. W. BETH
A. HEYTING
Editors
1959
NORTH-HOLLAND PUBLISHING COMPANY
AMSTERDAMTHE 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
AMSTKUDAMNo this book beofpart may reproduced
in orany form by microfilm anyprint,
other means without written permission
thefrom publisher
PRINTED IN THK NETHERLANDSCONTENTS
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 ........... 204VI 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.