Mathematical Rigour and Informal Proof

Cover
Title page
Copyright page
Mathematical Rigour and Informal Proof
Contents
1 Prologue: Three Proofs?
Proof 1: Sums of Odd Integers
Proof 2: Malfatti’s Marble Problem
Proof 3: Hex Numbers
2 Introduction
2.1 The Purposes of Rigour
2.2 Rigour in Principle and in Practice
2.3 Rigour Pluralism
2.4 The History of Rigour
2.5 Outline
3 The Standard View: Rigour as Formality
3.1 Introduction
3.2 Filling in the Gaps
3.3 Aims for the Standard View
3.4 Hamami’s Routine Translations
3.5 In Principle Formalisability
3.6 The Derivation-Indicator View
3.7 Criticisms of the Standard View
3.7.1 No Formal System
3.7.2 Incompleteness and Inconsistency
3.7.3 Unformalisable proofs and Faithfulness
3.7.4 Knowledge and Explanatory Redundancy
3.7.5 Overgeneration
3.7.6 The Mismatch Argument
3.7.7 Larvor’s Regress
3.8 True Essences and Modelling
4 Arguments and Dialogues
4.1 Introduction
4.2 Proofs as Arguments
4.3 Proofs and Refutations
4.4 The Dialogical Model of Proofs
4.5 Conclusion
5 The Recipe Model of Proofs
5.1 Introduction
5.2 Imperatives and Instructions
5.3 Diagrams and Instructions
5.4 Epistemology of Proofs
5.5 What Kind of Actions?
5.6 Rigorous Recipes
5.7 Conclusion
6 Rigour Is a Virtue
6.1 Introduction
6.2 Mathematical Epistemic Virtues
6.3 Rigour and Justice
6.4 Conclusion
7 Conclusion
References
Acknowledgements