Contents

1. Cover
2. Half Title
3. Title Page
4. Copyright Page
5. Dedication
6. Table of Contents
7. Preface
8. Introduction
9. 1. Economics and mathematics: Image, context and development
   1. Introduction
   2. Political arithmetic: the emergence of quantification of socio-economic phenomena
   3. From political arithmetic to political economy: the Enlightenment and beyond
   4. The triumph of formalism: from Walras to Debreu and beyond
   5. Notes
10. 2. Walras’ programme: The Walras–Poincaré correspondence reassessed
    1. Introduction
    2. The Walrasian programme in the context of the moral sciences
    3. The Walras–Poincaré correspondence, Phase I: the mathematisation of economics
    4. The Walrasian–Poincaré correspondence, Phase II: the measurement of utility
    5. The Walras–Poincaré correspondence, Phase III: Poincaré’s hierarchy of reservations
    6. Walras’ ‘Economics and Mechanics’ in the context of his platonic-scientific realism
    7. Mathematical physics as a deductive a priori science: Walras’ response to the Poincaré critique
    8. Conclusion: Walras’ ontological lock-in
    9. Notes
11. 3. The formalisation of economics and Debreu’s philosophy of mathematics
    1. Introduction
    2. Core theses: a preliminary account
    3. Debreu on the contemporary period of economic formalism
    4. Debreu and the achievement of rigour
    5. Debreu and the achievement of generality
    6. Debreu, simplicity and existence proofs
    7. Debreu’s global view of the mathematisation of economics
    8. Debreu’s proof of the existence of equilibrium and the Poincaré malaise
    9. Debreu, Walras and the proof of the existence of equilibrium
    10. Notes
12. 4. The axiomatic method in the foundations of mathematics: Implications for economics
    1. Introduction
    2. Rigour and axiomatisation
    3. The applied mathematical sciences and axiomatisation
    4. Debreu’s formalist mathematisation of economic theory
    5. Debreu’s mathematical model: formalist or semanticist?
    6. Debreu’s formalist philosophy of economic analysis: its assets
    7. Notes
13. 5. Hahn and Kaldor on the neo-Walrasian formalisation of economics
    1. Introduction
    2. The role of economic theory
    3. Hahn’s grammar of argumentation: the first step
    4. Axioms, assumptions and the grammar of argumentation
    5. Kaldor on Debreu’s achievement and legacy
    6. Notes
14. 6. Rationality and conventions in economics and in mathematics
    1. Introduction
    2. Hume, convention and the foundations of justice
    3. Lewis, convention and neo-classical rationality
    4. Keynes and post-Keynesians on uncertainty and conventions
    5. Ontological-epistemic indeterminacy, conventions and the philosophy of mathematics
    6. Conclusion
    7. Notes
15. 7. The emergence of constructive and computable mathematics: New directions for the formalisation of economics?
    1. Introduction
    2. Strict intuitionism and the neo-Walrasian programme
    3. The Bourbaki critique of Brouwerian intuitionism
    4. Dummett’s philosophical reconstruction of strict intuitionism
    5. Pragmatic intuitionism and economic theorising
    6. The internal critique of formalism and economic theorising
    7. Gödel’s theorems and Debreu’s philosophy of economic theorising
    8. Turing, algorithms and the mathematisation of economics
    9. An algorithmetic revolution in economic theorising?
    10. Notes
16. 8. Economics, mathematics and science: Philosophical reflections
    1. Introduction
    2. In praise of the philosophy of mathematics
    3. Philosophy of mathematics: a new formalisation of economic theorising?
17. Appendix
18. Bibliography
19. Index

Preface

Introduction

1    Economics and mathematics: Image, context and development

2    Walras’ programme: The Walras–Poincaré correspondence reassessed

3    The formalisation of economics and Debreu’s philosophy of mathematics

4    The axiomatic method in the foundations of mathematics: Implications for economics

5    Hahn and Kaldor on the neo-Walrasian formalisation of economics

6    Rationality and conventions in economics and in mathematics

7    The emergence of constructive and computable mathematics: New directions for the formalisation of economics?

8    Economics, mathematics and science: Philosophical reflections

Appendix

Bibliography

Index

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