Buch, Englisch, 624 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1056 g
Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel
Buch, Englisch, 624 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1056 g
ISBN: 978-0-691-05858-0
Verlag: Princeton University Press
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913).This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI.Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials.Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
Autoren/Hrsg.
Fachgebiete
- Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
- Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
- Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
- Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
Weitere Infos & Material
CHAPTER 1 Explanations 1.1 Sallies 3 1.2 Scope and limits of the book 3 1.2.1 An outline history 3 1.2.2 Mathematical aspects 4 1.2.3 Historical presentation 6 1.2.4 Other logics, mathematics and philosophies 7 1.3 Citations, terminology and notations 1.3.1 References and the bibliography 9 1.3.2 Translations, quotations and notations 10 1.4 Permissions and acknowledgements 11 CHAPTER 2 Preludes: Algebraic Logic and Mathematical Analysis up to 1870 2.1 Plan of the chapter 14 2.2 `Logique' and algebras in French mathematics 14 2.2.1 The `logique' and clarity of `ideologie' 14 2.2.2 Lagrange's algebraic philosophy 15 2.2.3 The many senses of `analysis' 17 2.2.4 Two Lagrangian algebras: functional equations and differential operators 17 2.2.5 Autonomy for the new algebras 19 2.3 Some English algebraists and logicians 20 2.3.1 A Cambridge revival: the `Analytical Society, Lacroix, and the professing of algebras 20 2.3.2 The advocacy of algebras by Babbage, Herschel and Peacock 20 2.3.3 An Oxford movement: Whately and the professing of logic 22 2.4 A London pioneer: De Morgan on algebras and logic 25 2.4.1 Summary of his life 25 2.4.2 De Morgan's philosophies of algebra 25 2.4.3 De Morgan's logical career 26 2.4.4 De Morgan's contributions to the foundations of logic 27 2.4.5 Beyond the syllogism 29 2.4.6 Contretemps over `the quantification of the predicate' 30 2.4.7 The logic of two place relations, 1860 32 2.4.8 Analogies between logic and mathematics 35 2.4.9 De Morgan's theory of collections 36 2.5 A Lincoln outsider: Boole on logic as applied mathematics 37 2.5.1 Summary of his career 37 2.5.2 Boole's `general method in analysis' 1844 39 2.5.3 The mathematical analysis of logic, 1847. `elective symbols' and laws 40 2.5.4 `Nothing' and the `Universe' 42 2.5.5 Propositions, expansion theorems, and solutions 43 2.5.6 The laws of thought, 1854: modified principles and extended methods 46 2.5.7 Boole's new theory of propositions 49 2.5.8 The character of Boole's system 50 2.5.9 Boole's search for mathematical roots 53 2.6 The semi-followers of Boole 54 2.6.1 Some initial reactions to Boole's theory 54 2.6.2 The reformulation by Jevons 56 2.6.3 Jevons versus Boole 59 2.6.4 Followers of Boole and/or Jevons 60 2.7 Cauchy, Weierstrass and the rise of mathematical analysis 63 2.7.1 Different traditions in the calculus 63 2.7.2 Cauchy and the Ecole Polytechnique 64 2.7.3 The gradual adoption and adaptation of Cauchy's new tradition 67 2.7.4 The refinements of Weierstrass and his followers 68 2.8 Judgement and supplement 70 2.8.1 Mathematical analysis versus algebraic logic 70 2.8.2 The places of Kant and Bolzano 71 CHAPTER 3 Cantor: Mathematics as Mengenlehre 3.1 Prefaces 75 3.1.1 Plan of the chapter 75 3.1.2 Cantor's career 75 3.2 The launching of the Mengenlehre, 1870-1883 79 3.2.1 Riemann's thesis: the realm of discontinuous functions 79 3.2.2 Heine on trigonometric series and the real line, 1870-1872 81 3.2.3 Cantor's extension of Heine's findings, 1870-1872 83 3.2.4 Dedekind on irrational numbers, 1872 85 3.2.5 Cantor on line and plane, 1874-1877 88 3.2.6 Infinite numbers and the topology of linear sets, 1878-1883 89 3.2.7 The Grundlagen, 1883: the construction of number-classes 92 3.2.8 The Grundlagen: the definition of continuity 95 3.2.9 The successor to the Grundlagen, 1884 96 3.3 Cantor's Acta mathematica phase, 1883-1885 97 3.3.1 Mittag-Lefler and the French translations, 1883 97 3.3.2 Unpublished and published 'communications' 1884-1885 98 3.3.3 Order-types and partial derivatives in the `communications' 100 3.3.4 Commentators on Cantor, 1883-1885 102 3.4 The extension of the Mengenlehre, 1886-1897 103 3.4.1 Dedekind's developing set theory, 1888 103 3.4.2 Dedekind's chains of integers 105 3.4.3 Dedekind's philosophy of arithmetic 107 3.4.4 Cantor's philosophy of the infinite, 1886-1888 109 3.4.5 Cantor's new definitions of numbers 110 3.4.6 C
