Philosophy of Mathematics and Economics by Boylan, Thomas A. -- Read -- Imperial Library of Trantor

Index

Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface Introduction 1. Economics and mathematics: Image, context and development

Introduction Political arithmetic: the emergence of quantification of socio-economic phenomena From political arithmetic to political economy: the Enlightenment and beyond The triumph of formalism: from Walras to Debreu and beyond Notes

2. Walras’ programme: The Walras–Poincaré correspondence reassessed

Introduction The Walrasian programme in the context of the moral sciences The Walras–Poincaré correspondence, Phase I: the mathematisation of economics The Walrasian–Poincaré correspondence, Phase II: the measurement of utility The Walras–Poincaré correspondence, Phase III: Poincaré’s hierarchy of reservations Walras’ ‘Economics and Mechanics’ in the context of his platonic-scientific realism Mathematical physics as a deductive a priori science: Walras’ response to the Poincaré critique Conclusion: Walras’ ontological lock-in Notes

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

Introduction Core theses: a preliminary account Debreu on the contemporary period of economic formalism Debreu and the achievement of rigour Debreu and the achievement of generality Debreu, simplicity and existence proofs Debreu’s global view of the mathematisation of economics Debreu’s proof of the existence of equilibrium and the Poincaré malaise Debreu, Walras and the proof of the existence of equilibrium Notes

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

Introduction Rigour and axiomatisation The applied mathematical sciences and axiomatisation Debreu’s formalist mathematisation of economic theory Debreu’s mathematical model: formalist or semanticist? Debreu’s formalist philosophy of economic analysis: its assets Notes

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

Introduction The role of economic theory Hahn’s grammar of argumentation: the first step Axioms, assumptions and the grammar of argumentation Kaldor on Debreu’s achievement and legacy Notes

6. Rationality and conventions in economics and in mathematics

Introduction Hume, convention and the foundations of justice Lewis, convention and neo-classical rationality Keynes and post-Keynesians on uncertainty and conventions Ontological-epistemic indeterminacy, conventions and the philosophy of mathematics Conclusion Notes

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

Introduction Strict intuitionism and the neo-Walrasian programme The Bourbaki critique of Brouwerian intuitionism Dummett’s philosophical reconstruction of strict intuitionism Pragmatic intuitionism and economic theorising The internal critique of formalism and economic theorising Gödel’s theorems and Debreu’s philosophy of economic theorising Turing, algorithms and the mathematisation of economics An algorithmetic revolution in economic theorising? Notes

8. Economics, mathematics and science: Philosophical reflections

Introduction In praise of the philosophy of mathematics Philosophy of mathematics: a new formalisation of economic theorising?

Appendix Bibliography Index

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