Relevant Arithmetic and Mathematical Pluralism

In The Consistency of Arithmetic and elsewhere, Meyer claims to “repeal” Goedel’s second incompleteness theorem. In this paper, I review his argument, and then consider two ways of understanding it: from the perspective of mathematical pluralism and monism, respectively. Is relevant arithmetic just another legitimate practice among many, or is it a rival of its classical counterpart—a corrective to Goedel, setting us back on the path to the (One) True Arithmetic? To help answer, I sketch a few worked examples from relevant mathematics, to see what a non-classical (re)formulation of mathematics might look like in practice. I conclude that, while it is unlikely that relevant arithmetic describes past and present mathematical practice, and so might be most acceptable as a pluralist enterprise, it may yet prescribe a more monistic future venture

Introduction

This is the introduction to the special issue on Robert K. Meyer and the philosophy of arithmetic

Relevant Arithmetic and Mathematical Pluralism

In The Consistency of Arithmetic and elsewhere, Meyer claims to “repeal” Goedel’s second incompleteness theorem. In this paper, I review his argument, and then consider two ways of understanding it: from the perspective of mathematical pluralism and monism, respectively. Is relevant arithmetic just another legitimate practice among many, or is it a rival of its classical counterpart—a corrective to Goedel, setting us back on the path to the (One) True Arithmetic? To help answer, I sketch a few worked examples from relevant mathematics, to see what a non-classical (re)formulation of mathematics might look like in practice. I conclude that, while it is unlikely that relevant arithmetic describes past and present mathematical practice, and so might be most acceptable as a pluralist enterprise, it may yet prescribe a more monistic future venture

Robert Meyer's Publications on Relevant Arithmetic

This is a bibliography of R.K. Meyer's published articles on relevant arithmetic

Robert Meyer's Publications on Relevant Arithmetic

This is a bibliography of R.K. Meyer's published articles on relevant arithmetic

The macroeconomics of imperfect capital markets. Whither saving-investment imbalances?

Starting with Wicksell and until the heyday of Keynesian economics, inflation, unemployment and business cycles were thought and taught mainly as problems originating from "saving-investment imbalances" due to some form of malfunctioning of the capital market. Whereas modern studies of imperfect capital markets have greatly improved our understanding of capital market failures, their impact on macroeconomics has remained surprisingly limited. The macroeconomic consequences of saving-investment imbalances are still undeveloped in this literature The most popular macroeconomic model to date - the so-called New Neoclassical Synthesis - dispenses with capital market imperfections altogether. The aim of this paper is fill this gap. Section 2 overviews the historical foundations and the current state of the macroeconomics of imperfect capital markets. Section 3 presents a competitive, flex-price model of saving-investment imbalances where deviations of the market interest rate from the Wicksellian natural rate generate (disequilibrium) business cycles. In section 4, the model is extended in order to make the market interest rate endogenous. This extension also allows preliminary considerations to be made about monetary policy and the control of the interest rate over the business cycle. Section 5 summarizes and concludes.