The Search for Mathematical Roots, 1870-1940 (eBook)

Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

Ivor Grattan-Guinness (Autor)

eBook Download: PDF | EPUB

2011
624 Seiten
Princeton University Press (Verlag)
978-1-4008-2404-5 (ISBN)

Infos

I. Grattan-Guinness is Professor of the History of Mathematics and Logic at Middlesex University. Founder of the journal History and Philosophy of Logic and past President of the British Society for the History of Mathematics, he has authored or edited numerous books, including The Norton History of Mathematics, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, and Convolutions in French Mathematics, 1800-1840.

---

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, Schroder, 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 Godel. 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 GodeI. 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.

Produkt-Details

• Erscheint lt. Verlag: 11.2.2011
• Zusatzinfo: 16 tables, 4 halftones, 3 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• Schlagworte: abstract algebra • Addition • Adjective • Algebra • algebraic logic • Ambiguity • American Mathematical Society • Analogy • arithmetic • Axiom • axiomatic system • Axiom of choice • axiom of infinity • Axiom of reducibility • Begriffsschrift • Big O notation • Cantor's Diagonal Argument • cardinal number • Charles Sanders Peirce • commutative property • complex number • Continuum Hypothesis • Contradiction • Edmund Husserl • Empiricism • Epistemology • Ernst Zermelo • existence theorem • existential quantification • Explanation • Foundations of mathematics • Function (mathematics) • Geometry • Georg Cantor • Gottlob Frege • inference • Infinitesimal • infinity • Integer • Intuitionism • irrational number • Law of thought • Lecture • Logic • Logical connective • Logical disjunction • logicism • Mathematical Analysis • Mathematical Induction • Mathematical Logic • Mathematical Theory • mathematician • Mathematics • Mathematische Annalen • metalogic • metamathematics • model Theory • Nachlass • Negation • Notation • Number Theory • Ordinal arithmetic • Pamphlet • Peano axioms • Philosopher • Philosophy • Philosophy of Arithmetic • philosophy of mathematics • Predicate (mathematical logic) • Principia Mathematica • Proof theory • Propositional Calculus • Propositional function • Publication • Pure Mathematics • Quantification (science) • Quantifier (logic) • Quantity • Rational number • real number • reason • reductionism • Rule of inference • Russell's paradox • scientific notation • set theory • Sheffer stroke • Special case • syllogism • Term logic • Textbook • Theorem • theory • The Philosopher • Transfinite number • Type Theory • Variable (mathematics) • Vicious circle principle • Well-order • Writing
• ISBN-10: 1-4008-2404-4 / 1400824044
• ISBN-13: 978-1-4008-2404-5 / 9781400824045