Giuseppe Peano Between Mathematics and Logic : Proceeding of the International Conference in Honour of Giuseppe Peano on the 150th Anniversary of His Birth and the Centennial of the Formulario Mathematico Torino (Italy) October 2-3, 2008

This book contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University to celebrate the 150th anniversary of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, a great attempt to systematise Mathematics in symbolic form. Cover......Page 1 Giuseppe Peano between Mathematics and Logic......Page 4 ISBN 9788847018358......Page 5 Preface......Page 6 List of Contributors......Page 8 Table of Contents ......Page 10 1.1 Peano and Classical Analysis......Page 12 1.2 Symbolic Writing and New Directions of Research......Page 15 1.3 Peano and Analysis after 1900......Page 17 1.4 Peano and Functional Analysis......Page 22 2.1 Introduction......Page 24 2.2 Peano, Gilbert and the Mean Value Theorem......Page 25 2.3 Peano, Mansion and Foundations of Calculus......Page 31 2.4 Peano, de La Vallée Poussin and Ordinary Differential Equations......Page 32 2.5 Peano, de La Vallée Poussin and Generalized Derivatives......Page 34 2.6 Appendix......Page 38 3.1 Introduction......Page 40 3.2 Peano’s Works on Numerical Analysis......Page 43 3.3 Integral Representation of Remainders......Page 45 3.4 Applications of the Remainder Functional......Page 49 3.5 Trapezoidal and Parabolic Formulas......Page 54 4.1 Prehistory......Page 58 4.2 Dedekind......Page 61 The New Method......Page 65 The Concept of Number......Page 69 Consistency......Page 71 4.4 The School of Peano......Page 74 5.1 Grassmann’s Legacy Background......Page 80 5.2 Peano’s Calcolo geometrico......Page 81 5.3 The Minimum System......Page 87 5.4 The Axiomatic Foundations of Geometry......Page 89 5.5 Conclusion......Page 92 6 The Formulario between Mathematics and History......Page 94 6.1 The Genesis and Aims of the Formulario......Page 95 6.2 The Influence of Leibniz......Page 99 6.3 The Stages of the Production of the Formulario......Page 104 6.4 Outcome of the Formulario and Cultural Spin-off......Page 112 7.1 Three Early Mathematical Interests......Page 146 7.2 Peano on ‘Classes’......Page 148 7.3 Peano’s Unsung Quantification Theory......Page 149 7.4 Two Further Figures......Page 150 7.5 On the Aftermath......Page 151 8 At the Origins of Metalogic......Page 154 9.1 Introduction......Page 168 9.2 Projective Geometry. Two Different Views......Page 169 9.3 Geometry of Position, according to Pieri......Page 170 9.4 Comparing Peano 1894c to Pieri 1895–1896 Notes......Page 172 9.5 Affinities and Segmental Transformations......Page 175 9.6 Conclusion......Page 178 References......Page 182 Index of Names......Page 198 List of Illustrations......Page 204 Contains The Papers Developing Out The Presentations Given At The International Conference Organized By The Torino Academy Of Sciences And The Department Of Mathematics Giuseppe Peano Of The Torino University To Celebrate The 150th Anniversary Of G. Peano's Birth - One Of The Greatest Figures In Modern Mathematics And Logic And The Most Important Mathematical Logician In Italy - A Century After The Publication Of Formulario Mathematico, A Great Attempt To Systematise Mathematics In Symbolic Form. Giuseppe Peano And Mathematical Analysis In Italy / F. Skof -- Some Contributions Of Peano To Analysis In The Light Of The Work Of Belgian Mathematicians / J. Mawhin -- Peano, His School And Numerical Analysis / G. Allasia -- Geometric Calculus And Geometry Foundations In Peano / G. Lolli -- The Formulario Between Mathematics And History / C. S. Roero -- Giuseppe Peano: A Revolutionary In Symbolic Logic? / I. Grattan-guinness -- At The Origins Of Metalogic / E. Casari -- Foundations Of Geometry In The School Of Peano / E. A. Marchisotto. Editor, Fulvia Skof. Includes Bibliographical References (p. 171-186) And Index. Contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University to celebrate the 150th anniversary of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, a great attempt to systematise Mathematics in symbolic form-- Source other than Library of Congress