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Towards a Philosophy of Real Mathematics.

By: Publisher: Cambridge : Cambridge University Press, 2003Copyright date: ©2003Description: 1 online resource (300 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511148897
Subject(s): Genre/Form: Additional physical formats: Print version:: Towards a Philosophy of Real MathematicsDDC classification:
  • 510.1
LOC classification:
  • QA8.4 .C67 2003
Online resources:
Contents:
Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- CHAPTER 1 Introduction: a role for history -- 1.1 REAL MATHEMATICS -- 1.2 THE CURRENT STATE OF PLAY -- 1.3 THE FOUNDATIONALIST FILTER -- 1.4 NEW DEBATES FOR THE PHILOSOPHY OF MATHEMATICS -- 1.5 TOWARDS A PHILOSOPHY OF REAL MATHEMATICS -- 1.6 RELATIONS WITH THE PHILOSOPHY OF PHYSICS -- 1.7 FACTORS GOVERNING THE WAY MATHEMATICS PROCEEDS -- 1.8 OUTLINE OF THE BOOK -- PART I Human and artificial mathematicians -- CHAPTER 2 Communicating with automated theorem provers -- 2.1 INTRODUCTION -- 2.2 AUTOMATED MATHEMATICAL REASONING -- 2.3 THE ARGONNE PARADIGM -- 2.4 THE ROBBINS PROBLEM -- 2.5 REFORMULATION -- 2.6 CONCLUSION -- CHAPTER 3 Automated conjecture formation -- 3.1 INTRODUCTION -- 3.2 COMBINATORIAL ENUMERATION -- 3.3 NUMERICAL IDENTITIES AND ENUMERATION -- 3.4 INDUCTIVE LOGIC PROGRAMMING -- 3.5 THE PROBLEM OF THE HOMOTOPY GROUPS OF THE SPHERES -- 3.6 RESULTS AND DIAGNOSIS -- Independent sources -- Language -- 3.7 CONCLUSION -- CHAPTER 4 The role of analogy in mathematics -- 4.1 INTRODUCTION -- 4.2 THOUGHTS ON ANALOGY -- 4.3 THE ANALOGY BETWEEN NUMBER AND FUNCTION -- 4.4 A WATERSHED IN THE USE OF ANALOGY -- 4.5 CONCLUSION -- PART II Plausibility, uncertainty and probability -- CHAPTER 5 Bayesianism in mathematics -- 5.1 INTRODUCTION -- 5.2 PROBABILITY THEORY AS LOGIC -- 5.3 QUANTITATIVE BAYESIANISM -- 5.4 WHAT MIGHT BE ACHIEVED BY BAYESIANISM IN MATHEMATICS -- Analogy -- Strategy -- Enumerative induction -- 5.5 CONCLUSION -- CHAPTER 6 Uncertainty in mathematics and science -- 6.1 INTRODUCTION -- 6.2 FOUR CASE STUDIES OF THE INTERRELATIONSHIP BETWEEN THE PLAUSIBILITY OF SCIENTIFIC HYPOTHESES AND EVIDENCE AND THE… -- The stability of the solar system -- The onset of turbulence -- The Lee-Yang circle theorem -- Quantum field theory.
6.3 MATHEMATICS AND SCIENTIFIC MODELS -- 6.4 THE PROBLEM OF OLD EVIDENCE -- 6.5 CONCLUSION -- PART III The growth of mathematics -- CHAPTER 7 Lakatos's philosophy of mathematics -- 7.1 INTRODUCTION -- 7.2 LAKATO'S STAGES OF DEVELOPMENT -- 7.3 THE METHOD OF PROOFS AND REFUTATIONS -- 7.4 THE RESEARCH PROGRAMME STAGE -- 7.5 LAKATOS ON RIGOUR -- 7.6 THE JAFFE-QUINN DEBATE -- 7.7 CONCLUSION -- CHAPTER 8 Beyond the methodology of mathematical research programmes -- 8.1 INTRODUCTION -- 8.2 PUTTING THE METHODOLOGY OF MATHEMATICAL RESEARCH PROGRAMMES TO THE TEST -- 8.3 DEDEKIND VERSUS KRONECKER -- 8.4 OTHER ATTEMPTS TO CONSTRUCT A METHODOLOGY OF MATHEMATICAL RESEARCH PROGRAMMES -- 8.5 KOETSIER AND THE METHODOLOGY OF MATHEMATICAL RESEARCH TRADITIONS -- 8.6 MADDY'S NATURALISM -- 8.7 CONCLUSION -- CHAPTER 9 The importance of mathematical conceptualisation -- 9.1 VALUES IN MATHEMATICS -- 9.2 WHAT IS A GROUPOID? -- 9.3 HOW GROUPOIDS COMPARE WITH GROUPS -- 9.4 THE FULL EXPLOITATION OF ONE-DIMENSIONALITY -- 9.5 GROUPOID ALGEBRAS USED TO COMPENSATE FOR BAD SPACES -- 9.6 APPLICATIONS AND OLD CONJECTURES -- 9.7 NEW PROSPECTS: HIGHER-DIMENSIONAL ALGEBRA -- 9.8 THE CONCEPTUAL AND THE NATURAL -- 9.9 CONCLUSION -- PART IV The interpretation of mathematics -- CAHPTER 10 Higher-dimensional algebra -- 10.1 INTRODUCTION -- 10.2 CATEGORIFICATION: MAKING DISTINCTIONS -- 10.3 HIGHER-DIMENSIONAL ALGEBRA AS AN ORGANISING LANGUAGE -- 10.4 DIAGRAMMATIC CALCULATION -- 10.5 APPLICATIONS -- 10.6 CONCLUSION -- Appendix -- MONOID -- GROUP -- RING -- IDEAL -- FIELD -- ALGEBRA -- COALGEBRA -- BIALGEBRA -- HOPF ALGEBRA -- CATEGORY -- FUNCTOR -- ADJOINT FUNCTORS -- MORITA EQUIVALENCE -- Bibliography -- Index.
Summary: Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics.
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Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF0006137
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP0006137
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Ebrary Ebrary Tunisia Available
Total holds: 0

Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- CHAPTER 1 Introduction: a role for history -- 1.1 REAL MATHEMATICS -- 1.2 THE CURRENT STATE OF PLAY -- 1.3 THE FOUNDATIONALIST FILTER -- 1.4 NEW DEBATES FOR THE PHILOSOPHY OF MATHEMATICS -- 1.5 TOWARDS A PHILOSOPHY OF REAL MATHEMATICS -- 1.6 RELATIONS WITH THE PHILOSOPHY OF PHYSICS -- 1.7 FACTORS GOVERNING THE WAY MATHEMATICS PROCEEDS -- 1.8 OUTLINE OF THE BOOK -- PART I Human and artificial mathematicians -- CHAPTER 2 Communicating with automated theorem provers -- 2.1 INTRODUCTION -- 2.2 AUTOMATED MATHEMATICAL REASONING -- 2.3 THE ARGONNE PARADIGM -- 2.4 THE ROBBINS PROBLEM -- 2.5 REFORMULATION -- 2.6 CONCLUSION -- CHAPTER 3 Automated conjecture formation -- 3.1 INTRODUCTION -- 3.2 COMBINATORIAL ENUMERATION -- 3.3 NUMERICAL IDENTITIES AND ENUMERATION -- 3.4 INDUCTIVE LOGIC PROGRAMMING -- 3.5 THE PROBLEM OF THE HOMOTOPY GROUPS OF THE SPHERES -- 3.6 RESULTS AND DIAGNOSIS -- Independent sources -- Language -- 3.7 CONCLUSION -- CHAPTER 4 The role of analogy in mathematics -- 4.1 INTRODUCTION -- 4.2 THOUGHTS ON ANALOGY -- 4.3 THE ANALOGY BETWEEN NUMBER AND FUNCTION -- 4.4 A WATERSHED IN THE USE OF ANALOGY -- 4.5 CONCLUSION -- PART II Plausibility, uncertainty and probability -- CHAPTER 5 Bayesianism in mathematics -- 5.1 INTRODUCTION -- 5.2 PROBABILITY THEORY AS LOGIC -- 5.3 QUANTITATIVE BAYESIANISM -- 5.4 WHAT MIGHT BE ACHIEVED BY BAYESIANISM IN MATHEMATICS -- Analogy -- Strategy -- Enumerative induction -- 5.5 CONCLUSION -- CHAPTER 6 Uncertainty in mathematics and science -- 6.1 INTRODUCTION -- 6.2 FOUR CASE STUDIES OF THE INTERRELATIONSHIP BETWEEN THE PLAUSIBILITY OF SCIENTIFIC HYPOTHESES AND EVIDENCE AND THE… -- The stability of the solar system -- The onset of turbulence -- The Lee-Yang circle theorem -- Quantum field theory.

6.3 MATHEMATICS AND SCIENTIFIC MODELS -- 6.4 THE PROBLEM OF OLD EVIDENCE -- 6.5 CONCLUSION -- PART III The growth of mathematics -- CHAPTER 7 Lakatos's philosophy of mathematics -- 7.1 INTRODUCTION -- 7.2 LAKATO'S STAGES OF DEVELOPMENT -- 7.3 THE METHOD OF PROOFS AND REFUTATIONS -- 7.4 THE RESEARCH PROGRAMME STAGE -- 7.5 LAKATOS ON RIGOUR -- 7.6 THE JAFFE-QUINN DEBATE -- 7.7 CONCLUSION -- CHAPTER 8 Beyond the methodology of mathematical research programmes -- 8.1 INTRODUCTION -- 8.2 PUTTING THE METHODOLOGY OF MATHEMATICAL RESEARCH PROGRAMMES TO THE TEST -- 8.3 DEDEKIND VERSUS KRONECKER -- 8.4 OTHER ATTEMPTS TO CONSTRUCT A METHODOLOGY OF MATHEMATICAL RESEARCH PROGRAMMES -- 8.5 KOETSIER AND THE METHODOLOGY OF MATHEMATICAL RESEARCH TRADITIONS -- 8.6 MADDY'S NATURALISM -- 8.7 CONCLUSION -- CHAPTER 9 The importance of mathematical conceptualisation -- 9.1 VALUES IN MATHEMATICS -- 9.2 WHAT IS A GROUPOID? -- 9.3 HOW GROUPOIDS COMPARE WITH GROUPS -- 9.4 THE FULL EXPLOITATION OF ONE-DIMENSIONALITY -- 9.5 GROUPOID ALGEBRAS USED TO COMPENSATE FOR BAD SPACES -- 9.6 APPLICATIONS AND OLD CONJECTURES -- 9.7 NEW PROSPECTS: HIGHER-DIMENSIONAL ALGEBRA -- 9.8 THE CONCEPTUAL AND THE NATURAL -- 9.9 CONCLUSION -- PART IV The interpretation of mathematics -- CAHPTER 10 Higher-dimensional algebra -- 10.1 INTRODUCTION -- 10.2 CATEGORIFICATION: MAKING DISTINCTIONS -- 10.3 HIGHER-DIMENSIONAL ALGEBRA AS AN ORGANISING LANGUAGE -- 10.4 DIAGRAMMATIC CALCULATION -- 10.5 APPLICATIONS -- 10.6 CONCLUSION -- Appendix -- MONOID -- GROUP -- RING -- IDEAL -- FIELD -- ALGEBRA -- COALGEBRA -- BIALGEBRA -- HOPF ALGEBRA -- CATEGORY -- FUNCTOR -- ADJOINT FUNCTORS -- MORITA EQUIVALENCE -- Bibliography -- Index.

Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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