The Search for Mathematical Roots, 1870-1940 Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Godel

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...

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Hlavní autor:	I. GRATTAN-GUINNESS
Médium:	E-kniha
Jazyk:	angličtina
Vydáno:	Princeton, NJ Princeton University Press 11.02.2011
Témata:	19th century 20th century Abstract algebra Addition Algebra Algebraic logic American Mathematical Society Arithmetic Axiom Axiom of choice Axiom of infinity Axiom of reducibility Axiomatic system Cantor's diagonal argument Cardinal number Continuum hypothesis Contradiction Edmund Husserl Epistemology Ernst Zermelo Existential quantification Explanation Foundations Foundations of mathematics Function (mathematics) Geometry Gottlob Frege History Inference Integer Intuitionism Irrational number Lecture Logic Logic, Symbolic and mathematical Logical connective Logical disjunction Logicism Mathematical analysis Mathematical induction Mathematical logic Mathematical theory Mathematician MATHEMATICS MATHEMATICS / History & Philosophy MATHEMATICS / Logic Mathematische Annalen Metamathematics Model theory Negation Notation Number theory Peano axioms Philosopher Philosophy of mathematics Predicate (mathematical logic) Propositional calculus Propositional function Pure mathematics Quantification (science) Quantifier (logic) Real number Reason Russell's paradox Scientific notation Set theory Sheffer stroke Syllogism Textbook Theorem Theory Transfinite number Type theory Variable (mathematics) Well-order Writing Axiom of reducibility Lecture Explanation Cantor's diagonal argument Algebraic logic Foundations of mathematics Quantification (science) Algebra Axiomatic system Mathematical analysis Mathematical induction Mathematical theory Russell's paradox Logical connective Axiom Contradiction Well-order Addition Real number Mathematische Annalen Inference Publication Philosopher Propositional calculus Predicate (mathematical logic) Function (mathematics) Existential quantification Syllogism Cardinal number Model theory Irrational number Textbook Quantifier (logic) Propositional function Axiom of choice Arithmetic Type theory Philosophy of mathematics Logical disjunction Negation Epistemology Theory Sheffer stroke Intuitionism Mathematics Notation Reason Metamathematics Pure mathematics Theorem Logic Continuum hypothesis Peano axioms Logicism Mathematician Edmund Husserl Geometry Variable (mathematics) Integer Transfinite number Axiom of infinity Abstract algebra Writing Set theory Mathematical logic American Mathematical Society Gottlob Frege Scientific notation Number theory Ernst Zermelo
ISBN:	9780691058580, 069105858X, 1400824044, 9781400824045
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Front Matter Table of Contents CHAPTER 1: Explanations CHAPTER 2: Preludes: CHAPTER 3: Cantor: CHAPTER 4: Parallel Processes in set Theory, Logics and Axiomatics, 1870s–1900s CHAPTER 5: Peano: CHAPTER 6: Russell’s Way In: CHAPTER 7: Russell and Whitehead Seek the Principia Mathematica, 1903–1913 CHAPTER 8: The Influence and Place of Logicism, 1910–1930 CHAPTER 9: Postludes: CHAPTER 10: The Fate of the Search CHAPTER 11: Transcription of Manuscripts BIBLIOGRAPHY INDEX
CHAPTER 6. Russell’s Way In: From Certainty to Paradoxes, 1895–1903
CHAPTER 1. Explanations
CHAPTER 7. Russell and Whitehead Seek the Principia Mathematica, 1903–1913
CHAPTER 8. The Influence and Place of Logicism, 1910–1930
CHAPTER 10. The Fate of the Search
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CHAPTER 5. Peano: the Formulary of Mathematics
CONTENTS
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BIBLIOGRAPHY
CHAPTER 2. Preludes: Algebraic Logic and Mathematical Analysis up to 1870
CHAPTER 4. Parallel Processes in Set Theory, Logics and Axiomatics, 1870s–1900s
Frontmatter --
CHAPTER 9. Postludes: Mathematical Logic and Logicism in the 1930s
INDEX
CHAPTER 3. Cantor: Mathematics as Mengenlehre
CHAPTER 11. Transcription of Manuscripts